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mkdir: Permission denied in /usr/lib with root user

I was trying to do apt upgrade what exceeded with some errors. Now, I found the reason why: Even root cannot write to /usr/lib and can create /usr/lib/policykit-1

But why? At least root should be able to write in every directory, right?

I’m running Debian 11 on a vServer. This error appeared unexpectedly and isn’t disappearing after rebooting multiple times or doing stuff like apt autoremove (this exceeds in a similar error).

Do you have some good ideas? If you need more informations, let me know!

Regards!