Unable to sign into my Apple TV after a reset

I've had an Apple TV 3 (A1469) in my home gym (connected to a TV) for awhile. Pretty much the only thing it did was stream music from my iMac as I worked out but I would occasionally use it to stream video from my iPhone using AirPlay. It worked well with no complaints.

I recently got Apple One which includes Fitness+ so I thought it was a good time to upgrade. I replaced the Apple TV 3 with a new Apple TV 4K, set it up, and no issues there.

I then decided to repurpose the Apple TV 3 to our entertainment room, using it more or less solely as an AirPlay receiver so my daughter can watch her YouTube videos on the big screen. I dutifully signed out of my Apple ID on the Apple TV 3, performed a full restore on it to bring it back to factory condition, then went through the setup process which included giving the device a new (unique) name. My daughter wasn't around so I didn't have her Apple ID password so I left it alone. I signed into our Prime and Netflix accounts so she could watch those services on it and that worked.

I enabled AirPlay with no password required and was surprised to discover that I could no longer stream anything (audio, video, or display mirroring) from my iPhone (15 Pro) to the Apple TV 3. My other Bluetooth and AirPlay-enabled devices in the house work just fine. The Apple TV 3 simply doesn't show up as an available streaming device.

I thought perhaps it needed an Apple ID for some reason so when my daughter was available we tried to login to her Apple ID -- and ran into a second problem. The Apple TV wouldn't allow her to login to iCloud. We'd enter her (valid) Apple ID and her (known good) password, it would send a code to her iPhone, we'd enter that into the Apple TV 3, and then get an error that her account wasn't set up with iCloud (or something along those lines) which makes zero sense. We ARE able to connect to the iTunes Store using her Apple ID and password. It's only when trying to login via iCloud does this error appear.

I searched around and found an uncomfortably large number of people having this error, including some very recent (within the past few months). Many of these people say they contacted Apple who told them it was a known issue with a fix forthcoming. I then called Apple to report the same issue and after maybe 10 minutes of discussion I was told the same thing -- it's a known issue and Apple is working on a fix.

When I go into Settings - General - About I see "Activation - Failed" listed. I can't honestly say that this wasn't there before the reset, but considering that I was able to login to my iCloud account and use the device for streaming before the factory reset I'm going to go out on a limb here and say that activation was fine when I set it up in the gym a few years ago and it's only now after being factory reset that it failed,

Both of these functionalities were working properly before I performed the factory reset. I know it's not a network issue as the Apple TV 3 is literally about 10 feet away from where it used to be in the gym, with exactly the same stuff between it and the router as it was before. Signal strength is good and there's no network errors being generated. It's not something unique to my phone; I also tried a MacBook and two iPads and none of them can see the Apple TV 3 while all of them could see it before I performed the reset.

So is there an actual fix for this

[Edited by Moderator]