It does on iOS, but I believe the onus is on the app developer to enable the autofill feature in the form, or at least make sure that the app hints to iOS that it can be filled with a password. I'm making that assumption because there are lots of apps which don't trigger the native Apple password manager either (which is a lousy user experience). However, if one works then both do. The UI offers a choice of password manager and Face ID works to unlock it.

I use both. Apple's manager supports OTP generation which is nice, but on desktop websites, Firefox is often more convenient.