Warning: unable to close filehandle GEN4 properly: No space left on device at /usr/share/perl5/PVE/APIServer/Any

Your situation appears rather odd. bbgeek has linked you to info on a file being locked by an ongoing process. I'm not sure that that is your problem - since it appears you have only deleted archived files.

Maybe your fs has somehow gone r/o. Probably try rebooting. Then check space.

As I've noted above I can't see where your standard Proxmox logging is going - this also needs dealing with.

I see you are using PVE 6.2 - this has already been EOL for three years (IIRC).