iCloud device verification failure on Macbook with 'Some iCloud data isn't syncing' error

"Some iCloud data isn't Syncing" - Unable to access some iCloud data on Macbook because iCloud device verification keeps "failing"

Device/network details: Macbook M1 Pro, 2021, Sequoia 15.6.1. 1TB SSD, 16GB ram. 14" display. Wi-Fi connection to home network, no VPN.

Had an issue undownloading a folder from iCloud that I had set to "Keep downloaded" to free up space on local Macbook SSD. Recommendations were to sign out and back into iCloud. Upon signing back in, I'm getting an error in System Settings that "Some iCloud Data Isn't Syncing". When I click "Resume Data Sync", I'm prompted to enter my Macbook password. Upon successful password entry, the message "Updating your account..." appears for close to a minute. I'm then prompted to enter the passcode for my iPad, under the same iCloud account, which I enter correctly. System Settings processes this for a minute, then says "Verification failed, there was an error verifying the passcode of your iPad". I retest with a false passcode, and within 7 seconds or so, I receive the error "Incorrect Passcode, please enter the iPad passcode again". This effectively proves I'm entering the correct password, and the verification just fails.

I've tried verifying with my iPhone passcode, my Macbook password, all to the same error of verification failed, not incorrect passcode. Eventually I'm hit with the "You've enter this password incorrectly too many times", even though we've more or less shown it's not my password that's the issue but the system. System restart and repetition yielded no different results.

Any advice for fixing this? Am I doing something drastically wrong here? Thanks for the help.

P.S. random detail but all my apps are "timed out" as if there was a time limit set and I've reached that limit. Have to say ignore limit to open apps like Google Chrome, however, messages won't let me click on either option. Still just stuck on "Time Limit". So far most other apps have let me hit "Ignore limit for today" and then "OK" will get me into the app. Messages has yet to allow this.

[Re-Titled by Moderator]