Up until last week I used my iPhone’s hotspot to connect an Apple TV 3, after upgrading to iOS 15 it stopped working. Is this because an ATV3 can’t connect to WPA3? I have tried the compatibility with older devices option and it didn’t work either.
This is likely due to a bug in some older WPA2 based devices that keep them from connecting to a "WPA2/WPA3 Transitional" network.
I had this same issue connecting an old ATV3 to my new Asus access point when I set it up in WPA2/WPA3 Transitional mode. Other old WPA2 devices can connect, but due to a bug in the ATV3's WiFi code, it can't connect. I suspect the same issue is happening with it trying to connect to your iPhone's hotspot, which now uses WPA2/WPA3 transitional mode.
My solution with the Asus access point was to split out the 2.4GHz network and set it to use WPA2 authentication only. Then I put my ancient devices like the ATV3, an old TiVo and such on the 2.4GHz network. All the modern stuff lives on the 5GHz network which uses 2/3 transitional. Sadly I don't think you can set what mode the iPhone's hotspot is using.
One thing that makes me sad about the ATV3 in particular is that Apple has released a few security updates for the old ATV3 in the past couple of years, so they could have released a fix for the WPA2/WPA3 connection bug. But they did not. ATV3's are still useful as AirPlay targets; they should have fixed this issue. Oh well, time marches on I guess.