They do, but the absence of that integration is not breaking either the shell or the app. The integration
breaks because the shell relies on seeing the apps’ settings schemas, which are not exported by Flatpak.
Arguably, settings that are shared between the shell and apps like this are not app-specific in the first place, and should be in a desktop-wide shared schema. In the past, these things could just be muddled through.
The proper isolation of Flatpak exposes this for what it is: a hack
This is worth filing a bug about. We should fix up the first-login experience, one way or another.