Well last night my Spectrum internet went down again for several hours, so I had no choice but to either watch streaming services like Hulu live TV on my iPhone 13 Pro Max or iPad Air 2020 via hotspot, or try to get the iPhone hotspot to work with my ATV 4K 2017. Eventually I did get it to work, but it took a few tries and some fiddling about to figure out the exact way to make it work. Like the OP's experience, it didn't seem to want to display in the ATV 4K list of Wi-Fi networks available. First of course, I had to unplug the ethernet cable so it would even consider Wi-Fi networks. I forgot to write down exactly what worked, my bad and my apologies, but I think this is what I finally did:
On my iPhone 13 Pro Max:
- In Settings --> Wi-Fi turned OFF Wi-Fi on my iPhone 13 Pro Max. (Note, this might not be necessary, but I was trying all sorts of things in frustration.)
- In Settings --> Personal Hotspot turned ON Allow Others to Join.
- In Settings --> Personal Hotspot turned ON Maximize Compatibility.
Note: I think turning on hotspot access turned my Wi-Fi back on. I remember it had to be on to communicate with the ATV 4K 2017.
On my ATV 4K 2017:
- In Settings I went to the network area and eventually the iPhone hotspot popped up as an option. So I selected it and the connection worked. (Note, with the Maximize Compatibility option on my iPhone 13 Pro Max turned OFF I could never get the hotspot to display, but when I turned that ON it did display.)
Unfortunately, the ATV 4K was displaying a lower resolution and pixelating quite often. In frustration I returned to my iPhone 13 Pro Max and in Settings --> Personal Hotspot turned OFF Maximize Compatibility. As soon as I did that the ATV 4K screen started using high definition and looked as good as ever. Go figure! So turn ON Maximize Compatibility so the hotspot can be seen by the ATV 4K, but after selecting it and getting it working, turn Maximize Compatibility back to off to improve the picture. It must send more data when turned off.
Note that my iPhone 13 Pro Max is using T-Mobile, and the new 5G through T-Mobile gives me over 300 Mbits internet speed. I watched the ATV 4K for about two hours via my hotspot with no issues at all using both Hulu Live TV app and BritBox. So yes it works, but it was a PITA to get it to work, but once I did it worked flawlessly. Hopefully I will remember how I did it if I ever need to do it again, and with Spectrum internet going down often, I probably will need to do it again.