Unable to log out of Apple Account on MacBook Air due to an error

Hey,

First post on here.

This evening, I've been having some trouble with my Apple ID and my MacBook.

I have signed in to my MacBook Air with the same Apple ID I use on my iPhone 14 Plus, which has Screen Time Restrictions set up. (this is not the problem as you'll see later on)

I need to sign out of my Apple ID and into my organisation's Apple ID, however, when I attempted to do so, I discovered my profile was greyed out. Following the guidance of another post on here, I managed to fix that problem on both my iPhone and my MacBook through enabling "Accounts" in Screen Time Restrictions settings. Then, I've encountered my current problem of the "Log out" button being greyed out. "Media and Purchases" and "Devices" are also greyed out too.

I tried to fix this by going to accounts.apple.com and signing in using my personal Apple ID, and removing my laptop from Find My on my Apple ID, however, I suspect this has further exacerbated the problem.

Every 10-15 minutes, I'm getting a prompt telling me "This Mac can't connect to iCloud because of a problem with "(insert iCloud address)"." and "Open Apple Account settings to fix this problem.". This then causes the System Settings application on my Mac to completely freeze up, and when I go to force quit the application, unlike what usually happens when an app becomes unresponsive (in red text next to the name of the app, "Unresponsive" or something similar,) it doesn't display any signs of the app becoming unresponsive.

I've removed Screen Time entirely from my Apple ID, so this clearly is not the problem. (from my understanding)

What should I attempt next?

Factory resetting my MacBook isn't just a last resort in this scenario, it is only an option when I've truly cooked (done proper damage) to my MacBook that can ONLY be resolved through a factory reset - realistically, this is only an option if it is ABSOLUTELY DEFINITELY the only thing that can be done.

Help is desperately needed and any assistance is heavily appreciated!!!

Thanks

Noah

[Re-Titled by Moderator]