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Although I'm in the same boat (just started using hilt and multi modules last week) I haven't integrated DI into the other modules yet...

But you didn't really ask a question... do you have anything specific?

In my current project, we do not use dagger outside modules. I.e. we use dagger internally only in modules. Outside modules only usual interfaces are available.
For module gluing we use Component Holder pattern.
Further reading:
<https://proandroiddev.com/modularization-of-android-applications-in-2021-a79a590d5e5b>
Example: <https://github.com/PavelSidyakin/WeatherForecast>

Yes we use dagger in multi module, we just migrated to Hilt, previously just using subcomponents. Do you have a specific question or issue?

componentholder looks fine but there is more boilerplate

I use dagger in my multi module project . my module is daynamic feature  . it is too hard

My main confusion w/ dagger espec. in multi module is every app/team does it very different. I think that is the main sales pitch of hilt