I fail to see how navigating an app is fundamentally different than navigating the site presented by groups.io. They would both have menus to access the different group areas.
In my opinion, it's way out of scope for groups.io, of little value, and very expensive.
see -> https://savvyapps.com/blog/how-much-does-app-cost-massive-review-pricing-budget-considerations
I added a shortcut on my home screen on my phone, 4 taps got me to the files section listing in one of my groups.... (no login necessary as that was cached)