We are using OSM maps via Mapbox to display bikecycle paths in different cities we (Lyft Bikes and Scooters) operate. Here is an example in the Bay Area : https://member.fordgobike.com/map/
We have made in the past a few small edits following the feedback of users or local transportation departments.
Imports into OSM are never simple, ultimately because you have to manually merge the new information with the existing features, and it’s very very easy to get it wrong. (It’s also really easy to piss off the local contributors!) Consequently there are detailed guidelines you must follow before carrying out any import.