The Polish, and Baltic, UK and Romanian view is that Putin is going to escalate anyway - for them it's an argument over whether, by putting up an umbrella, you make it rain...
For those eastern states, as well as having a huge pool of familial ties to Ukraine, shared experiences, and a far deeper level of political and societal solidarity with Ukraine, there's the very real practicality that despite Russia beginning to get it's shit in order, and even if/when they win, the war itself, and the economic sanctions, have done a huge amount of damage to the Russian Army.
The longer the Ukrainians are able to stay in the fight, the worse that damage gets. The worse that damage gets, the less effective the Russian Army will be against the eastern states when Russia tries it on with them.
For the eastern states, this is as much their war as it is Ukraine's.