No, installing apps is just genuinely bad UX, at least for me, because my password manager doesn't work in apps, and I have to manually generate and copy and paste password. If creators of the app are extra stupid, they make it so that you cannot paste into the password input, so I have to enter the generated password character by character.
And why is it broken? Is there a way for a password manager app to somehow inspect other apps and identify forms within them and interact with the forms?
...yes? I can't tell if you're trolling at this point or genuinely unaware.
Both iOS and Android have APIs for this, you (as the app developer) just mark the relevant fields in the app as login/password/etc, and the OS will interact with your chosen password manager to autofill and/or save them.
If you've never seen this work on your device, then you might have something configured incorrectly — many app developers are incompetent and bad at this; but not _all_ of them.
It works for filling an existing password, but not for creating a new one, iOS still prompts me to fill existing even though I'm on the sign up page. On the web 1Password can also automatically generate a Fastmail masked email address, but I doubt there's any hope for that to work in a native app.