Hi Aeraesoria,
Thanks for posting in Apple Support Communities.
We understand you're unable to sign out of your Apple ID on your Mac. To address this behavior, restart your computer to refresh running processes.
Put your Mac in safe mode and try signing out if this continues after restarting. Safe mode will limit the software allowed to run while running a health check on your Startup disk.
Before you begin
To start up your Mac in safe mode, you need to know what type of Mac you have.
1. On your Mac, choose Apple menu > About This Mac.
2. Look at the information in the window to determine what type of Mac you have:
* If you see an item labeled Chip, followed by the name of the chip, you have a Mac with Apple silicon.
* If you see an item labeled Processor, followed by the name of an Intel processor, you have an Intel-based Mac.
5. Use the corresponding set of instructions below to start up your Mac in safe mode.
Start up your Mac with Apple silicon in safe mode
1. On your Mac, choose Apple menu > Shut Down.
2. Wait for your Mac to shut down completely. A Mac is completely shut down when the screen is black and any lights (including in the Touch Bar) are off.
3. Press and hold the power button on your Mac until “Loading startup options” appears.
4. Select a volume.
5. Press and hold the Shift key, then click Continue in Safe Mode.
6. The computer restarts automatically. When the login window appears, you should see “Safe Boot” in the menu bar.
Start up your Intel-based Mac in safe mode
1. Turn on or restart your Mac, then immediately press and hold the Shift key until you see the login window.
2. Log in to your Mac.
3. You might be asked to log in again.
4. On either the first or second login window, you should see “Safe Boot” in the menu bar.
You can find these steps and more in Start up your Mac in safe mode - Apple Support.
Regards.