Do not support admin password

Part 1 of 2

Use the Terminal command below .

Though, the Issue of Administrator Password issue will remain.

>> sudo softwareupdate -i -a -R <<

Credit goes to @leroydouglas

Part 2 of 2

Generally, the very First Account used to Setup the Computer the Very First Time, is both the Owner Account and the Administrator Account of this computer

Below may be too Technical but worth mentioning just the same

The " Owner Account of this computer "  has that privilege to add, remove, upgrade or downgrade accounts. This would include adding more Admin Accounts and / or downgrading an ADDED Admin account 

Set up users, guests, and groups on Mac

Normally the " Owner Account  " is the very first Account used when the Computer was Very First Setup as New and out of the box.

Adding additional Admin Account can be done there after.

Below link all provide additional insights about the Difference between Admin Accounts and Owner Accounts  

https://eclecticlight.co/2021/07/18/last-week-on-my-mac-the-perils-of-m1-ownership/

This article from Apple specific to Apple Silicon Computer

link below

Use macOS Recovery on a Mac with Apple silicon - Apple Support (CA)

Excerpt from above link

• Edited "  Reinstall macOS on your computer. In the Recovery app, select Reinstall macOS Monterey "

In Theory ,this should download the Latest Version of Monterey

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading. It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance 

3 - Can you Log into the computer Administrator Account

4 - If yes suggest this Terminal Command below to Verify this account is an Administrator Account will all the privileges

id -Gn username | grep -q -w admin && echo True || echo False

If the $USER  is admin then True will result.

Credit to @VikingOSX

Suggest updating the Existing Monterey 12.3.1 to the current stable version 12.6.3 First

The computer may work far better in the upGrade process with a fully updated version

Links below specific to this issue

About the security content of macOS Monterey 12.6.3 - Apple Support (CA)

Keep your Mac up to date - Apple Support (CA)

Your account seems to be an administrator, as it should.

Please tell us exactly what OS version you have and what are you trying to update to.

Also: what is your mac model and year? These determine which updates it can use.

If you are unsure: from the Apple menu, choose About this Mac.

It will tell you - for example, it may say "MacBook Air (late 2013)" or something.

Welcome

Welcome and Thank you too