Hello Clock_Failure_macbook,
Isolating what is blocking the ability to change that setting to automatic would be our next step.
We would suggest starting up the system in what is called safe mode. Safe mode only loads what is needed to run the computer. This can help isolate what is causing issues.
To start in safe mode, follow these steps:
1. Turn on or restart your Mac, then immediately press and hold the Shift key as your Mac starts up.
2. Release the key when you see the login window, then log in to your Mac.
3. You might be asked to log in again. On either the first or second login window, you should see ”Safe Boot” in the upper-right corner of the window.
More information is available here: How to use safe mode on your Mac - Apple Support
The computer will take longer to start in safe mode, and the screen may have some distorted video as it starts up. This is normal. Once you are logged in, use the system and test to see if you can change the setting.
If everything seems to work as expected, go ahead and restart the computer normally and test again. There are steps outlined on what to do if the issue does or does not continue in safe mode.
Starting in safe mode also forces the computer to run some disk checks similar to First Aid. This can actually resolve some issues.
Have a good day.