I've looked at the TL for a bit. However, I have to wonder: just how was Russia able to get Armenia and Kurdistan? And even though the Ottomans got absolutely wrecked in Europe, would they still have some strength available to keep hold in Anatolia?
Armenians revolted to join their Orthodox Brothers-in-Arms in Russia, and the Kurds similarly revolted. They kept their independence initially because Russia had quite a bit of new land still to consolidate, but were still forced to align with Russia out of feat of being devoured by their neighbors.
I imagine that Russia's desire not to dive further into Anatolia would be similar as to why they wouldn't want to take over the Kurds directly, the need to consolidate. Also because Napoleon the Great would threaten another war with Russia. Once the French and Russians agreed to partition the Post-Turkish sphere in the 3rd Explorers' War, it was all over for their de-facto independence.
IMO Egypt should've also tried to gain independence during this time in order to take advantage of the chaos.
Assuming that you're talking about the fall of the Ottomans in the Early 1800's, Egypt did get independence.
Did you mean Syria? If so, Syria did try, but newly establish Turkish State was able to wrest control back from still-divided-among-themselves Syrians*
If you mean why Egypt isn't trying to get Independence as of the War of the Russian Succession, well there's big ol' giant French Army right next door. It wouldn't be a very pretty time for any rebel.
*Syria as of the War of the Russia Succession initially existed entirely because Russia propped them up, but after time consolidating, they can stand on their own two legs, as shown with King Fahd.
Also, considering how the Spanish American colonies wanted independence, wouldn't they not be colored blue?
I hand-waved this with A) Napoleon never overthrowing the Bourbon Monarchs, removing the initial spark that lit the Wars of Independence and B) Later Bourbon reforms rolling back on the caste system, removing some of the kindling, but enough remained for their still to be an underground Independence Movement.
admittedly, a lot of the first two maps were made just by pulling stuff out of arse and throwing it out there... Kinda just ran with it from there. I also kinda feat that I might be accidentally contradicting myself with some of this. Quite a lot to keep track of, you know, especially over the course of 3 years, on and off.