It's highly unlikely it will escalate to the point of nuclear war because of the concept of MAD (mutually-assured destruction) - if the Russians used nuclear weapons against NATO and its allies then NATO would retaliate with nuclear weapons against Russia.
MAD means that in a nuclear war, nobody "wins" because even the side that are the last man standing have a devastated world to rebuild.
Personally I think Russia will be satisfied when they've recaptured the territory lost when the USSR collapsed, i.e. they'll want Estonia, Latvia, Lithuania, Poland, Belarus, Czechia, Slovakia, Hungary, Romania, Moldova, Bulgaria, the countries that formerly made up Yugoslavia and Albania - either formally as part of Russia (eg Crimea) or a puppet state (eg Belarus). Once they've got these areas under control then I think they'll be satisfied that Russian "pride" is restored and the westernization of eastern Europe has been properly checked. I doubt they'd see the need to reclaim the east of Germany.
All this can be accomplished by a full scale war with non-nuclear weapons. Probably conventional weapons for the most part but also chemical/biological weapons if the Russians feel it's necessary.
My guess would be that Russia will take Ukraine relatively easily because sanctions from the West won't bother them. Once they start moving into the Baltic countries, Poland, Hungary etc. then NATO will be forced to use military force. There will probably be a very destructive war in eastern Europe as NATO and Russia battle it out, many lives will be lost and cities will be seriously damaged. Over time, a natural division will fall somewhere with no side able to advance significantly. This will probably lead to an uneasy peace, a new Iron Curtain going up, because claiming more ground would not be worth the price to either side.
It's unlikely to end up in a nuclear war though because NATO won't strike first and Putin isn't stupid enough. Of course, if new leaders come in, or there is an accidental deployment of nuclear weapons due to a systems glitch or human error, then it could become more realistic.