Standstill with Ukraine looks bad, and authoritarian regimes can survive almost anything except looking bad.
Responding to a NATO “attack” from Estonia, Putin can pivot to a bigger enemy where of course Russia has to employ universal conscription / nuclear weapons / whatever. The country must unite against this unprovoked western attack, etc, etc.
Nuclear weapons are no option. Russia would be wiped off the map before they could push that button.
A single Tomahawk missile could obliterate Moscow which would immediately end the war because Russia is extremely centralized. It's the reason almost 80% of all Russian SAM capability is stationed around the city.
Putin is unpredictable but he's not stupid. You don't become president of Russia by being stupid.