You don't have to use a closed source TOTP client such as Google's. There's RedHat's FreeOTP and there's another open source one called antOTP. You can find them on F-Droid as well.
There have been TOTP PAM modules for ages (these work on a Linux client and Linux server via e.g. SSH). You can even add YubiKey to PAM. Same for BSD Auth and macOS.
Try the "scan code" button which should activate the camera and the app will crash. I just tested it with my iPhone and verified. The iOS App Store application was last updated 4 years ago. There's also comments there saying it doesn't work anymore.
Reading / using existing codes might work properly, or manually inputting them.
Interestingly my wife's XS is having the problem you describe but not my X.
I've sent a note to the maintainers, but there's an open git issue for it. Not sure when their commits will roll to the store.
I'm told by multiple colleagues at redhat that they've raised this with internal support, so it should be sorted eventually. Lots of iphones in redhat and this is the app they officially support for TFA internally.
When I was researching, literally every article I read mentioned Google'S TOTP PAM module. I can't even find any other ones that have active development. Do you know of any? Would love to use another one if it works with my iOS authenticator app.
If you have an NFC YubiKey and an Android phone with NFC then the Yubico Authenticator is pretty awesome. You can store your OTP tokens on your YubiKey. Also open source.