I believe that you can't both simultaneously provide wifi hotspot and use wifi internet (at least, I couldn't on a phone several years ago last time I tried it). I think you can only do that if the network the phone is using is accessed via the cellular modem.
I absolutely can, that's how I connect my ps4 to my uni accommodation internet as it's mschapv2 or smth the ps4 can't connect to. I know it's definitely using the wifi and not my mobile data as my data usage for the day is unchanged after I've downloaded a game.
Cheap Chinese android phone from 2020 (or maybe 2021 can't remember).
Depends on the phone OS and wifi chipset Some Pixel phones can do it last I checked, which was about a year ago. It's a fragile dependency. For example, a Samsung with the same wifi chip didn't work.
