Also, will OSM - OrganicMaps\CoMaps will introduce any time soon ability for public transport routes?

I don't think there are any current plans for it. It's actually really difficult to get right.

OsmAnd kinda cheats and doesn't have any scheduling information, basically it assumes that the transit comes often enough that it doesn't matter, which is fine in bigger cities. However, if your bus comes only twice a day it will be an issue.

There's an open-source app for public transit called Bimba. It is a bit janky, and it requires you to be online for proper routing, but it does work for many cities. It still needs a lot of polishing before I'd consider it done, and actually I'd love for it to just become an OsmAnd plugin at some point.