1. Why would the British give up on ousting Napoleon?
2. Taking the Dutch colonies was not a problem as OTL, I'll give you that
3. Why would France overrun everything for the British?
4. How are they going to beat Russia on land? Napoleon tried but failed miserably?
5. How are the British going to turn the Ottoman Empire in a client state? Is Constantinople falls, the Ottoman Empire falls. The Ottomans in 1807-1808 were in no state to be turned into a client state. The governors of various provinces would refuse any pro-British demands, like they refused the reforms. Also, Neither the British or the French would have enough resources to subjugate the entire Empire and with Russia allowing it. If Russia can be beaten? See point 4. If Napoleon or any French ruler will do it? See point 3. Subjugating North Africa is not difficult yet not easy as well. In the sense of, taking the Coastal towns but that's it. France conquered Algiers in 1830 and only secured the small parts behind the coastal towns in the early 1850s. That's almost 20 years.
6. How are the British going to divide their resources in subjugating Mesopotamia AND Levant AND North Africa? That's plain impossible especially with their wars against the Maratha Confederacy by the EIC.
I am tired of reading. This seems like a plan someone has when playing Europa Universalis IV or Victoria II. It is not realistic. Not even the slightest bit. Most of the European and American Nations were not like the Zulu to subjugate with ease. Especially when you consider that France does most of the work in bringing down a European power like Russia.
You'll find me to be the farthest person from a Britwanker around, for starters. As to why they give up on ousting Napoleon, the premise involves a France-wank to begin with. France is far more successful in subjugating their defeated enemies such as Austria, and butterflies lead to a more well-planned invasion of Russia supported by an engorged Kingdom of Poland, Kingdom of Hungary, Sweden, etc. that topples the Czar and turns Russia south and east of Astrakhan into splinter states due to no central authority from St. Petersburg and no realistic means for the French to actually conquer these lands. So British public perception shifts to seeming despair or resignation in toppling Napoleon's regime in Europe when the last person standing is the Ottoman Empire and thus, a shift to containment.
3. They're not doing it for the British, the French are trying to counteract Britain's naval blockade by destabilizing their economy and forcing their trading partners into the Continental System. First Russia, then the Ottoman Empire. Britain probably teeters on bankruptcy in the early years of such a scenario.
4. See above premise about a Napoleon-wank
5. Political dependency shifting into economic domination. The Ottoman Empire will be dependent on Britain to keep France on the other side of the Straights and will be forced to relocate their capital, in all likelihood. Constantinople may or may not fall, what matters is that the Osmanli dynasty doesn't collapse but are put into a precarious enough situation that they're dependent on Britain and in turn, the British are dependent on the Ottomans to sell their goods to. By the time the Ottoman Empire starts prospering on their own, their economy is intertwined with Britain's and is basically the Left Hand of the UK in foreign policy and heavily influenced by British political thought. Anti-France, pro-navy, pro-colonialism. Basically part of the informal empire in spirit. Britain isn't seizing the Ottoman Empire by any means; you're putting words into my mouth(text) and reading what you want to read. Britain 'subjugating' North Africa or Persia doesn't mean setting up a British governor.
6. Britain and the Ottoman Empire are in bed together in what starts as political dependency(ie puppet) like mentioned above, Britain isn't conquering anything. You're out of your mind if you think that's what I wrote. You think I'd call Napoleon trying and largely failing to subjugate either Russia or the Ottoman Empire impossible, then turn around and say Britain can overrun thousands upon thousands of KM from Morocco to Bengal? Really?