First - get a back up now before you continue (or check you can restore from your existing backup and it is recent on key important data).
The main thing to do is not follow guides that don’t reflect the current hardware and software. I would suspect anything that relies on single user mode with macOS Catalina and newer and go back to basics.
What are you trying to accomplish and what does Apple support say about that topic?
Disk utility and terminal still work from recovery, so those are the tools I would use instead of single user mode for mounting.
Now on to your implied question. When you don’t have an admin account you either need to reset the password on an existing account or your system has failed in several manners.
Here are the Big Sur specific steps for account management and reset options. https://support.apple.com/guide/mac-help/reset-your-mac-login-password-mh35902/mac