StreetComplete is intentionally kept simple (for the most part). Also to keep data entry fast and accessible to beginners. As a consequence there are a few things that you cannot really tag with it, such as certain rare building types, rare surface values for paths, etc.

I've started out with StreetComplete too, and eventually graduated to more complex editing tools (mainly JOSM these days). But when outside there's not too many substitutes for what StreetComplete can do well.

Every Door (https://every-door.app/) may be able to set arbitrary values for the building tag, while still retaining a mostly simple interface.

I've fixed the building tag now, by the way :-)