Face ID is broken for authorizing app purchase in the App Store.
The App Store requires a password or even shows a pop-up that Face ID is not available, try again later. However, Face ID works perfectly fine for Pay, unlocking the iPhone and authentication in 3rd party apps like bank apps, messengers, etc.
Basic troubleshooting steps didn't resolve an issue.
Restoring my iPhone to factory settings and then restoring from iCloud also didn't resolve an issue.
Even restoring again and setting up as new doesn't help.
Created a report with Apple Advisor. Waiting for the fix.
Just checked it out now . Working fine for me .
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I haven't checked that earlier, but this option is available since watchOS 5 for sure.