This may not be the cleanest solution and I'll still leave this question as unsolved as it isn't fully understood in my opinion. Yet still I want to share my experience and how it worked out for me.

I modified it a little bit but I used the code from this post as minimal working example. I thought map_id has to be the same as activeMapType: map.supportedMapTypes[map_id] but this seems not to be the case. Using map_id = 1 and map.supportedMapTypes[0] resulted in the desired Street Map map type and using offline tiles.