My understanding is that a proxy war requires at least one of the belligerents to be acting through a proxy, not necessarily both. For example, here is a wiki page [0] about the Iran-Israel proxy conflict/war, which is fought between Israeli and Palestinian combatants.
Either way, this is a just a matter of how you choose to define the term.
The important point that I'm trying to make is that, while Ukraine is of course fighting for its own sake (not trying to claim here they are only a puppet or something - as is Palestine in the other example), it's also clear that NATO is massively involved in the conflict, with its own aims for the war which may or may not be entirely aligned with Ukraine's (or Ukrainians') best interests.
Either way, this is a just a matter of how you choose to define the term.
The important point that I'm trying to make is that, while Ukraine is of course fighting for its own sake (not trying to claim here they are only a puppet or something - as is Palestine in the other example), it's also clear that NATO is massively involved in the conflict, with its own aims for the war which may or may not be entirely aligned with Ukraine's (or Ukrainians') best interests.
[0] https://en.m.wikipedia.org/wiki/Iran%E2%80%93Israel_proxy_co...