Found a resolution: I had to *reset* (not restart) my AppleTV.
Background…
I had a Netflix account of my own, but closed it when I moved in with someone else that also HD a Netflix account. We decided I’d scrap my account and make a new profile on their account.
Tried to log in with the new account and got Error 113.
• Updated the iOS on my AppleTV
• Uninstalled and reinstalled my Netflix App
• Tried logging in while my VPN/DNS service was not active
• Tried resetting the password
• Tried contacting Netflix Support, they just told me to try all the things I’d already tried (resetting the password, then uninstalling and reinstalling the App)
I could log in fine with every other device except the AppleTV.
I tried logging in with my old account (the one that I ended my subscription on) and found I could log in with my old Netflix account just fine, but not the new one.
This told me that there must be a conflict with the AppleTV retaining some sort of data, and Netflix not liking me switching accounts. I tried resetting my AppleTV and I can now log in with the new account.
After the reset process was complete I set up my AppleTV using my iPhone rather than manually, which meant it remembered which Apps I had installed and the layout. 😍🙌