Thanks for your reply!
I found that Maplibre as “fork” of Mapbox is also a very viable option - it is open source and free, so no payments like with Mapbox if you exceed basic functionality. Maputnik as editor for styles is not too different from Mapbox studio, and I guess I’ll do my style work with Maputnik - but still in the learning phase, maybe I reconsider at some point.
Regarding getting the data, the tilemaker approach Nakaner pointed me at works nice and well (after some starting hickups - which are expected if a novice like me fumbles his way around).
My current feeling is that I now have all building blocks to do my project - and I’m happy about this. Will report back here when I have success and point to a full writeup.