My thoughts on the mobilization and the annexation with a side of implicit nuclear threats... I think that Putin has very good reasons to be suspicious of the commitment of the Russian people to this war, which is why he has tried very hard to limit the impact of the conflict by not conducting a mobilization and by not deploying conscripts into the conflict zone in any significant numbers. This partial mobilization is an admission that things are going poorly, which is not a surprise to anyone in the West and likely only a marginally greater surprise to many Russians. Given that Russia’s biggest problem right now is a lack of manpower, any steps to put more bodies onto the line is a good thing.
The problem is that the impact won’t be felt on the front lines for several months, and Ukraine now has a strong case for stepping up its pace of operations for the rest of the campaign season, which will last until early spring (things get tough in winter in Ukraine but they don’t stop entirely). Ukraine will also have a good story to sell to the West about how it needs both short-term assistance to conduct additional offensives as well as long-term support (fighter jets et al) because the war with Russia may continue for a good long while.
With respect to the nuclear threats… look, you can’t just grab chunks of another country, pretend to annex them, and then expect that the rest of the world is going to go along. Ukraine isn’t going to respect the new national border with either its fires or its personnel, and I very much doubt that Washington is going to try to impose discipline on this point.
I don’t see how this works out for Russia. I can certainly understand why Putin is doing this; he judges that the regime is at risk if it suffers a strategic defeat at the hands of Ukraine and the West, and so he needs to pull out all of the stops. Given the current economic and military situations, however, it hard to see how these cards help his hand.