A backyard swimming pool would not be considered a Badestelle in German, I suspect it wouldn’t be considered a badplats in Sweden either, and it probably wouldn’t be considered a leisure=bathing_place in OSM. A bathing_place is always in (or at?) a natural body of water such as a river, reservoir, lake or the sea.
The swimming pool can be tagged with leisure=swimming_pool, and then you can add sport=swimming if it’s suitable for competitive swimming, or more generally, for exercise (the OSM idea of what sport means is a bit wider than in English).