Maybe it works for you, but I’d be careful with those commands.
At least on macOS 12.3, the /tmp folder is a symlink to /private/tmp, which in turn is owned by root:wheel. That is for all intents and purposes correct owner and group. In turn, /private/tmp is writable by everyone. So normally, you should be able to create files in there.
If you can’t create any file in that folder, that means the permissions are not correct, and not the owner. By now changing the owner, everyone else may no longer be able to create files in there, which just means you solved one error by introducing another…