Unable to log in to System Settings on my iMac's administrator account using correct password

You may have this enabled causing the problem:

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

kiwijam2919 wrote:

When I login to System Settings on my administrator account, I cannot use the correct password to unlock settings even though the login recognizes it as the correct user password. This problem is occurring to that account only and does not occur on my other administrator accounts.

If we may ask for clarification " When I login to System Settings on my administrator account, "

One does not Log Into System Setting

System Setting are available only once the User has Logged into their account

Admin account normally is the First User Account used to Setup the computer when new

That same Original Admin Account  has that privilege to add, remove, upgrade or downgrade accounts. This would include adding more Admin Accounts and / or downgrading an ADDED Admin account 

Would suggest reviewing Which Admin Account was the Original Admin Account

As for Changing an Admin Password

Pretty sure, one needs to be Logged Into the "Admin Account 1 " to change the password for " Admin Account 1 "

Though, I have only 1 Admin Account which is also the Owner Account

Below link will 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/

Have you tried changing the PW on that account?