Russia did not “leave” 2nd coalition until Napoleon became the 1st Counsul. Paul was quite explicit about this: “Now, when France got a king in anything but name ...”. Improving relation with Russia was a reasonable idea for Napoleon but why would it ceased to be afterwards? You are seemingly missing what was written: Alexander’s envoy in Paris was an outspoken enemy of the French Revolution and Napoleon while his envoy to London was not just an ardent Anglophile but got an instruction to accept all British conditions. It was not just an act of improving relations.
Execution of d’Enghien did not produce any action in Germany but Alexander broke diplomatic relations with France using it as a pretext. Britain was at war with France since 1803 but it could not form the 3rd Coalition without Alexander’s eager participation and it can hardly “led” it without troops on the ground. The 3rd Coalition started with St-Petersburg treaty (Alexander Novosiltsev to London to start talks and conditions were f8nalized in St-Petersburg) between Russia and Britain (March 30, 1804) In parallel Alexander conducted secret talks with Austria and Sweden which resulted in them jo8ning the forming coalition (secret treaty with Austria - November 6, 1804 and treaty with Sweden - January 14, 1805). What were the Russian “national interests”? None whatsoever.
What were Russian interests in supporting the 4th Coalition and continued fighting after defeat of Prussia? None.
Talleyrand told Alexander <whatever> at Erfurt? What exactly could he tell him that Alexander already did not know? Alexander was looking for Napoleon’s help against the Ottomans but got none. How this could pass for Napoleon’s “machinations”? The CS was hurting interests of the Russian nobility (but not the “national interests” because it resulted in the lower bread prices and growth of the manufacturing) but Alexander bypassed the problem with Tariff of 1810, which was, BTW, explicitly anti-French.
Alexander did not join Austria in 1809? He could not: the Ottoman War was still going on and Russian army was reforming. But between Tilsit and 1812 Russian military budget increased 4 - 5 times and there were few massive levies increasing size of the field army 2 - 3 times.
In 1812 Napoleon attacked Russia, which was a mistake, but the relations already had been spoiled and Alexander was quite active in spoiling them.
As for 1813 - 14, you are just repeating a standard position of the western historians. In the early 1813 situation was not uniformly seen this way on the Russian side: while liberation of Prussia happened more or less spontaneous, the “Russian party” led by Kutuzov was against “liberation of Europe”. Kutuzov was quite explicit in his opinion that the further fighting would benefit Britain but not Russia. Chances of the second French invasion of Russia after experience of 1812 were minuscule.
Taking your observations in order. Russia's leaving the 2nd Coalition had more to do with being defeated at 2nd Zurich, and the changed strategic situation. You seem to belong to a school of history that explains most decisions by understanding the personal feelings of the leaders making them. This is sometimes called the "Great Man Theory of History. According to this theory great men make arbitrary decisions based on internal reasoning, with little input from external sources. Though this has sometimes been true most of the time there are larger forces driving events.
So you think Czar Paul left the Coalition because a Military Strongman had seized power in France? Since this hadn't changed French policy in Europe, this would seem to be a frivolous reason. But in your favor seeking revenge for abolishing the "Order of the Knights of St John" was pretty frivolous to. But wait the Military Strongman was the one who's dissolving of the Order, which provoked Paul to join the war to begin with. Now I'm confused, did Paul hate Napoleon, or like him because he was a King for all practical purposes?
Napoleon's attitude towards Russia changed because the situation changed. He always seemed to have a high personal opinion of the Czar Alexander, and gyrated between War & Peace for strategic reasons, not personal ones. From 1800-1811 Napoleon wanted peace with Russia, only in the lead up to 1812 did he want war. I didn't miss what people wrote about Alexander's choice of ambassadors, I dismissed it with a short comment, because it's not a meaningful, or insightful comment, it's just a data point.
Russian ambassadors were drawn from the Aristocratic Class. Some of them were pro, and some anti British, Alexander logically picked a pro-British ambassador, to improve Russo-British relations. He conceded to British terms because France was a more immediate threat to Russian interests. He would have been hard pressed to find an aristocrat who was pro French Revolution, or who had a personal fondness for a man an aristocrat would consider a boorish, upstart, who had seized power in a military coup. Russo French relations would have to be based on national interests, not warm personal feelings between diplomats, or shared national values. The United States never sent a Communist to serve as ambassador to the Soviet Union, or the PRC.
To say the d'Enghien affair produced no reaction outside Russia is to assume there is no state between amicable relations, and breaking them off. Russia had less to fear from French retaliation, then small vulnerable German States, or even Austria, so they could react more strongly. Your stating Alexander used the d'Enghien Affair has an accuse? If he'd wanted to go to war in 1802 he could have. Russian Fleets and troops could have helped the British in the Mediterranean, and conducted operations in Italy. Russian Troops with British help could have also landed in Holland, or North Germany. Operations of this type could've induced other powers to join an earlier Third Coalition.
Why would Russia enter into secret talks to form an anti-French alliance? Maybe for the same reason everyone else was doing it for. All the European Powers, except Spain were concerned that France was becoming too powerful. She'd annexed all the territories west of the Rhine, along with Switzerland, Large parts of Western Germany, and most of Mainland Italy were under French control, or domination. Revolutionary, & Napoleonic France had reached a level of territorial conquest, and military power vastly greater then anything achieved under Louis XIV.
Ideologically France was by it's nature a revolutionary regime, that posed an existential threat to all reactionary states. In the period leading up to the Third Coalition no one could be sure what exactly would be the nature of Napoleon's rule. Would he be a true liberator, or just a new monarch trying to secure his dynasty. Listen to Beethoven's 3rd. Several years later it was clear that the latter was the case, and the monarchs could, and did deal with him has a peer. The Emperor of Austria formed a dynastic alliance with France, by marrying his Daughter to Napoleon. Napoleon had first sought a Russian marriage, but it was the women, particularly Alexander's mother who prevented it. The Czar's mother was the Russian Royal who hated Napoleon, not her son.
Why did Russia try to help Prussia in 1806-7? They were still at war from the Third Coalition. The Russians weren't a party to the Treaty of Pressburg. They simple withdrew back to home territory under cover of the Armistice after Austerlitz. Russia kept fighting in Italy, along with the British, only withdrawing from Naples when the French sent heavy reinforcements to retake it.
It's was unfortunate for Prussia that Napoleon acted before any Russian Army could have rendered effective assistance. Once Austrian neutrality was secured Napoleon was ready to make his move. Prussia's mistake was not joining the Third Coalition, in the fall of 1805 when they could have cut Napoleon's communications across Germany. If they'd acted then Napoleon would have been forced to abandon Vienna, and fight a much less favorable campaign in Germany. There would be no Battle of Austerlitz.
Talleyrand could tell Alexander a lot. He told him not to trust Napoleon, that his ambitions were unlimited, and that he planned to use Austria has a counterweight to Russian power. He also told him Napoleon's advice to invade Turkey, and Persia were merely designed to tie them down, to keep them out of European Affairs. To hear that kind of advice from a foreign minister about his head of state must have been jarring. Talleyrand was continuously advising Napoleon to not overplay his hand, that he had to accept some type of balance of Power that took into account the interests of other powers. French Hegemony wasn't sustainable, because sooner or later every other power would challenge it. That was the policy he brought to Vienna in 1815.
The Continental System was certainly not beneficial to Russia. Your argument is based on a protectionist theory that industry will develop faster without foreign competition. Loss of export markets was putting a severe strain on Russian Finances, and deigning them goods, and technology not available on the Continent. Protectionist policies never work in the long run, the vast majority of economists reject it, The failure of the CS is just another historical example.
If it was such a boon to the Russian Economy, and standard of living of the peasants why did the Czar, and every other ruler, and official in Europe who could pay a bribe violate it? The French massively violated it themselves? By 1811 the Russians were almost completely ignoring it, which was the prime motivation for Napoleon to invade Russia. The CS cost Napoleon more then it gained him, and was a completely failed attempt at economic warfare.
In 1809 even 50,000-100,000 troops would have been decisive. Are you contending that Russia couldn't put 50,000 men in the field? The Austrian Government made it's decision for war at the beginning of February 1809, by the beginning of March it was an open secret in the diplomatic world, Napoleon know war was at hand, Russia knew as well. So with his deep personal hatred of Napoleon being his driving force since coming to the throne, with 3 months time to transfer troops from less critical fronts Alexander, with perhaps the biggest army in the world couldn't send 50,000 men toward Vienna? It's simple hard to believe.
Yes I'm repeating Western Historians, because they make logical sense. I know the decision to invade Poland, and liberate Germany wasn't universally supported by all Russian political, and military leaders. If not for the reasons I stated what was the Czar's motivation to take the option he did? Personal hatred? If he hadn't Napoleon would have crushed Prussia, in the Spring of 1813, and Austria would have stayed a French Ally. Napoleon would have driven the Russians out of the Grand Duchy of Warsaw, and been back on the Neiman by August. I agree that Napoleon would never have invade Russia again, but he could have diplomatically, and economically isolated her. No country wants to be put in that situation, and most would go to war to prevent it.
From your comments I take it your not from a Western Country, and have a different take on aspects of history. I really don't know what they teach in a Russian History Class about the Napoleonic Wars. I hope it's not as Russia Centric has their take on WWII, Russia did everything, and
everything was about Russia, and Russia was the only thing that mattered. With all the strategic considerations that the belligerents needed to consider, it's hard to believe that personal hatred was the driving force. It's also hard to believe that Russian historians are the only ones with the insight, or access to original records to prove this "Personal Hatred Theory". I don't think it stands up to critical analysis, but your free to defend it.