WI the Russians don't back the Ottomans during the first Ottoman-Egyptian war?

In 1831, Muhammad Ali of Egypt sent an invasion force commanded by his son Ibrahim into Syria. The modernized Egyptian army managed to overpower the Ottoman garrisons of Syria and easily beat back the reinforcements sent by the Sultan to check them, then proceeded to advance into Anatolia. The Ottomans, panicked, sent a large force against the Egyptians, in the process leaving Constantinople barely defended. However, despite outnumbering the Egyptians, the Ottoman vanguard was beaten badly at Konya and most of it was killed or captured. At that point, the Ottomans were in no position to stop the Egyptian advance and it seemed like a last-stand defense of Constantinople was imminent. At that point the Sultan Mahmud II sent a desperate appeal to the Russian Czar, the long-time rival of the Ottoman Empire. The Sultan offered generous terms, essentially granting the Russians control of the Bosporus straits (not directly, but allowing Russian warships to pass through the straits while giving the Czar the right to close the straits to ships of any other power, effectively turning the Black Sea into a Russian lake) in return for Russian intervention against Egypt. The Russians then proceeded to send warships into the Bosporus, blocking any attempted crossing by the Egyptians, and landed troops in Anatolia. The British and French - who up until that point turned a blind eye as they had their own business to take care of closer to home - now became alarmed, as it seemed like the Ottomans were about to become a Russian puppet, severely upsetting the balance of power. They forced the Ottomans to break their alliance with the Russians, in return for getting the Egyptians to stop the war. The Egyptians reluctantly agreed, but they got to keep all of Syria as well as their de-facto independence from Constantinople.

But what if it had gone the other way? France and Britain showed no interest in intervening on behalf of the Turks at first, despite appeals by the Sultan, only after they signed the Alliance with Russia did the Western powers become concerned. So what if the Russians instead decided on an even riskier gamble, and joined forces with the Egyptians in trying to weaken the Ottomans? Militarily, they likely could dismantle the Ottoman Empire completely at this point, but it would 1. likely lead to Western intervention anyway, maybe even Austrian intervention too; and 2. would have massive shockwaves, including possibly negative ones, on all of the middle east and eastern Europe. They don't have to totally partition the Ottoman Empire between them, but maybe just a partial partition, e.g. Egypt gets Syria, Arabia, and Iraq, and perhaps the South Anatolian coast, while Russia gets Armenia, Trebizond, Dobruja, and suzerainty over Serbia and the Danubian principalities.

I'd also be interested in what people think would happen if the Russian just decided not to intervene at all and let things play out.
My limited understanding is that the Russians really really want control of the Strait more than anything more than other territorial gains. Protecting their Orthodox brethren is ultimately secondary to preventing an Ottoman empire from becoming a puppet of France and Britain.

Now, I guess Muhammad Ali could offer the same deal (my understanding is that he could probably usurp the Ottoman empire himself). But that's probably to going to mean an early Crimean War.
This looks like a job for @alexmilman

(sorry, hate to do this to you yet again, but you probably have more insights on the actions of Nicky I than most of us do.... :))
Well, NI did what he was expected to do being himself (support of the legitimate regime and expectation of the benefits) so the question is about what he would do if he was not the OTL NI and anybody’s guess is as good as mine. 😜

Regarding potential international military confrontation, in the 1830s he would be much better off than in 1850s because technological gap was not there, army was not yet completely turned into the parade ground toy and the Russian finances still were in a good shape. France just got a new monarchy and it’s ability to go to war with Russia was quite limited, which means that Austria hardly would risk it either and this leaves only Britain, aka purely naval operations in the foreign waters.

Not sure that siding with a rebel would be ideologically acceptable for NI but doing nothing would weakening the Ottoman Empire anyway, regardless the outcome and as a puppet it was extremely unreliable one being vulnerable to the French and British pressure so the Russian-Ottoman agreements did not worth too much except for the cases of a direct annexation.

Value of the whole Straits thingy is anybody’s guess but as long as it could not be enforced by Russia, probably not high enough.

So, IMO, the best thing that NI could do would be to mind his own business and let the Ottomans and Egyptians to fight themselves into the exhaustion. The same goes for the Hungarian Revolution. But this would require a different Nicholas.