App Store, can't download/purchase with Face ID

Device: iPhone 13 (256 GB)

iOS ver.: 17.2.1

When downloading apps in App Store, it waits a while and doesn't even try to authenticate with Face ID, straight shows Install button, and asks for password for Apple ID. I've tried many different settings, relogging of Apple ID, nothing helped. Updating to newest iOS also did nothing, issue occured also on iOS 16.6. What is strange is that normal Face ID works fine, even in apps (fast and reliably). What could I try next? I'm not the only person with this issue, see comments on videos with title like "how to fix face id app store".