Built in apps - iMessage. And yes, that does seem to be in the app store now, however, there's a lot there that seems to be missing - access to photos for example isn't listed in the health card, neither is microphone access - both of which are core features of the app.
It looks like the way it's implemented, access to photos comes through a Photos extension to iMessage (I think I recall these being called "iMessage apps"?), rather than it being inherent to the app.
And options for the microphone similarly seem to belong either to the extensions, or to the system—which handles microphone input as a substitute for typing.
It's possible you're right, and I'm missing something, but that's how it appears to me.
Is that available to other apps? If not - then this just looks like they're skirting around things they foist on third party developers to make themselves look squeaky clean.
I don't know the details, but I know that third-party apps can add iMessage apps. And the microphone input to replace/supplement the keyboard is a systemwide thing, working on any(?) text input.
The microphone access is also for voice messages, which are supported by other messaging apps, but again, has to be listed in the health card - and looks nefarious.