apple tv 3d gen will not accept new password

Did you follow the steps mentioned in this related article?

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Apple TV

To play content from your Mac or PC on an Apple TV HD, go to Settings > Accounts > iCloud.

On Apple TV (3rd generation or earlier) go to Settings > iCloud.

• If you're signed out, choose Sign In. You'll be asked to sign in with the Apple ID that you entered for the iTunes Store. If you use the same Apple ID for iCloud and the iTunes Store, choose Yes.
• If you're signed in with your previous Apple ID, choose Sign Out, then choose Sign In. You'll be asked to sign in with the Apple ID that you entered for the iTunes Store. If you use the same Apple ID for iCloud and the iTunes Store, choose Yes.

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copied from: What to do after you change your Apple ID or password - Apple Support

If you have a legacy 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.