Can't log in to icloud and can't remove macbook

Last week, my Sierra older Macbook Air suddenly couldn't log into iCloud. Error messages including not being able to login to iCloud at that time, unexpected error, and Apple server error. I don't use anything on iCloud except Find my Mac, and couldn't turn that off on the laptop after several tries, but then it was suddenly off the next day, and yet I still couldn't log in.

In total, I tried the following:

• reboot
• safe mode
• move com.apple.system.preferences.plist to desktop and reboot
• move user's Library Keychain folder content to desktop and reboot
• move user's Library Cloud folder contents to desktop and reboot
• New admin account on computer
• try different Apple ID (even in new account)
• remove the laptop from the Find My Mac via website
• remove the laptop from my Devices on my account website

I spent three hours on the phone with Apple the next day doing much of these same things again. And when we would remove the device from Find My Mac or my Devices on the websites, the laptop would keep coming back every time the Mac connected to the internet again, even AFTER I was successfully able to log out on the computer when the Find My Mac on the computer suddenly unchecked itself. Sometimes a page refresh would show it still there as if Apple's server wouldn't delete it from my account.

I was transferred to a higher tier tech who suggested I reload the OS (not erase, just install OS). I did that, and it didn't work initially, but then I moved the preferences.plist and Keychain files to the desktop again, rebooted, and then I was finally able to log in fresh again. Everything seemed normal after that until today.

Today, I experienced my monthly Apple ID lockout (since 2020, my AppleID started to lock me out periodically. It went from once every few months to monthly to weekly, disappeared for a long time, and then came back last Fall, locking me out once a month again. Many people complained about this problem on this forum and concluded that it's a problem with Apple's servers and had no relationship to the OS, or if someone used 2FA).

After unlocking my ID and logging back in on my laptops and other devices, like always, that one laptop couldn't log in to iCloud again - Apple Server errors again. Tried reinstalling the OS and rebuilding the prefs file and Keychain again, but doesn't work (yet?). And unchecking Find My Mac or logging out of iCloud on the laptop still doesn't work. I also can't remove the laptop from Find My Mac website or my Devices again. Every time the laptop is back on the internet, it is re-added - and my laptop can be located, so it also online on the server even though I removed it. I had tried another of my laptops when I was on with Apple support, and it was removed without a problem. Apple servers won't delete the laptop from my account so I can re-add it.

So, I think the issue isn't with my computer, but with something on Apple's servers, but not sure what to do about that. If I update the OS this time (and was holding off because of some software), I am not convinced this will solve the problem if the issue is with Apple and not my device. Clearing out the Keychain apple ID file should make me have to log in from scratch again, but it isn't.

Any suggestions before I try updating the OS?