/var/log/pve/... path you mentioned in the initial post are part of pve-root. If your error message is about running out of space in that place, you want to check out the size of that partition. The default pve-root was allocated to be 94GB or something crazy for me using default isntallation. That was way too much, so I reduced my to 32GB. I don't know if you've set it to 1GB based on your message, but if so, that is way too little (I'm using about 1.6GB on my pve-root right now, for example, and I try not to install too many things on my host node), and you should see if there's a way for you to some how resize that or relocate it to another bigger drive.