Transit App works fantastic in urban US, Canada, Western Europe, Aus, NZ. (It's also great when visiting a new location for discovering which routes get you from A to B, speed/frequencey/cost, as opposed to commuters who already know which mode, route and stop they want, and primarily want real-time updates, ETAs. Obviously you can supplement it with the local transit app/website.)

There's not much patchworking/assembling once you bookmark your preferred locations, research what times they open/close, select favorite transit modes, bookmark specific lines, research which exact stops. Don't mentally lock into Google Maps as your primary thing.

I said the c) part is already done by Transit App and generally better than Google Maps (shows rideshare time-and-cost estimates, bikeshare/scooter pickup locations etc.) Where 'taxi' has generally been replaced by rideshare and by 'private bike networks' you mean bikeshare. Not sure if by 'private bus network' you mean coaches, or employee shuttles, but those are sometimes not open to the public.

As mentioned, the amount of local detail depends on how much your municipality participates in open-date initatives; if it doesn't, ask them to. Transit App is adding new regions constantly.