Does ubuntu still install snaps when you use apt?

Yup, what makes flatpak more akin to the open source spirit is that new submissions to flathub are open source and rely on a PR model

docs.flathub.org/docs/for-app-authors/submission/

github.com/flathub/flathub/pulls

And software that exists on flathub is open and accessible in their repositories

github.com/orgs/flathub/repositories

Whereas snaps are a web based walled garden controlled by canonical

snapcraft.io/docs/using-the-snap-store

They both provide benefit as you explained, but flathub (flatpak’s default repo) is definitely more open in how it is handled