I think that we should have a mysql tag, because sometimes we are facing problems with specifics databases systems.
For example, see the question Why we need the key property in the Upsert class if it is never used? which specifically deals with database in internals.
No, I do not think we need explicit tags for database backends.
One, I think the current database tag is sufficient here. There really is very little in Drupal that is database specific, and internals questions (like the one you referenced) are more about the implementation of the Database API.
My biggest fear is that people will start using database tags like the version tags to just say what database they are using.
