Applying to Baden-Württemberg universities as German National with foreign qualifications

This is probably too niche of question (why is why I couldn’t find an answer on the wiki) but has anyone else been in this same situation?

Schools in other states seem to have a process (usually though the application portal) where they recognize your credentials whereas schools in Baden-Württemberg link you to this government website: https://rp.baden-wuerttemberg.de/rps/abt7/zeugnisanerkennungsstelle/

My situation is more complicated because I earned a bachelor’s in history in the US but now would like to do a bachelors in science in Germany.

Does this mean I can skip the time consuming and expensive process of getting my high school diploma converted to HZB?

A bachelors degree obviously qualifies me to start university, but how do I get my bachelor’s degree recognized in Baden-Württemberg? Does Baden-Württemberg just follow the standard anabin.de process that other states do?

Any help at all would be much appreciated.