Check if you installed a program designed to manage who is the admin:
If you’re not using enterprise type managed tools, reports of this on recent OS have lessened.
For sure, don’t follow any old guides (like this) about removing /var/db/.AppleSetupDone after booting to single user mode.
Were this my Mac, I would immediately try to install macOS on an external drive to be sure your backup is good and seen from the new external OS before trying to finesse the system you have. Then I would call Apple support as I would know more about what’s broken and they would know I have the means to do a reinstall saving tons of time. Or I could ask them to fill in gaps in my process why I couldn’t do a reinstall.
If you’re sure your backup and erase is solid, you could experiment as follows:
If you can enter iCloud recovery mode and try resetting the password, that should be somewhat safe to attempt.
Here is an old guide that also might possibly work especially steps 2 and 3. Anything years before that will not work. You will have to finesse the system to getting the proper file system mounted in a state to reset the admin account permissions.
The big problem is your admin group isn’t designed to ever drop the last admin user, so who knows what else is broken on your OS. A reinstall is the prudent thing to do unless Apple Support has a great fix and can let you know they are seeing this as a specific bug with a limited scope of breakage and it’s not a sign of general failure of your OS (at least in terms of account management).
Of course if you know your backup is recent and good, you can start with erase install and just not worry why this happened. Your suggested process is solid and straightforward. Erase, import, move on and solve this only if it recurs.