I deauthorized all my computers, now I can't sign into my Apple TV box

I deauthorized all my computers, now I can't sign into my Apple TV box

Correlation is not causation. Something else is amiss.

The Apple TV box doesn’t care about authorizing computers or not.

Apple TV (1st generation)

The original model Apple TV box from 2007 [A1218] doesn’t work anymore for sign-ins (since 2018).

Identify your Apple TV model - Apple Support

Find your Apple TV model number - Apple Support

For [A1378, A1427, A1469]:

If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.

Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.