Your information is about 15 years old))) or someone is keeping you misinformed))) this term is no longer used in the current Russian political context... Chechnya receives a lot of money from the federal budget for infrastructure projects (IT IS a republic within Russia), i.e. it's not a rebel region, well currently it's a special donation area... The fertility rate there is the highest in Russia))).
I understand it is a republic of Russia. My understanding is that a low level Chechen insurgency continues even today. For example there was a 2010 attack in the Moscow Metro. My point is that if the Chechens received outside help, it is unlikely that Russia would respond with a nuclear weapon.

Even if the information is 15 years old, it still supports my point. So, fifteen years: (1)the Chechens were supported by the US, (2) Russia had nuclear weapons, and (3) Russia did not launch their nukes at the United States in retaliation for supporting the Chechens.

You mix up different things. Uprising is not subject of nuclear war at all. Regular army will supress something like Chechnia (and so it was). Talking about "Siberia uprising" is something like talking about "Kansas uprising". Not in this reality. In any case it is about INNER conflict.
China army inside Russia borders completely differs.
I think you misunderstand what I am insinuating here. I use "uprising" in quotation marks to indicate that it is not a real internal uprising, but an attack by China in the guise of an uprising. As you said, such an uprising would be suppressed by the regular army. However, if the insurgents have "captured" (in others words Chinese T-14s that were bought from Russia) T-14s, it will make things a lot more difficult for the Russian Army than it would have been if the insurgents didn't have T-14s.

In understand that such a small scale conflict would not result in the loss of all of Siberia, but it might result in some parts declaring independence, and then being supported by China as a new country.

It is easier for the Russian Army to suppress and insurgency if it is not equipped with the latest Russian equipment.