No idea if this has a proper name, but there certainly is a lot of catholic girls' school yuri/shoujo ai. Maria-sama ga Miteru and Strawberry Panic immediately come to mind. I believe that this style was very common in early yuri stories, to the extent that you can see a lot of modern authors referencing this formula as parody, or to deconstruct what is seen as an out-of-date and unrealistic cliche. Here are some suggestions that more-or-less fall into that category, with varying degrees of faithfulness:
Ouji-sama nante Iranai - I don't think this is a Catholic school, but it has that old-fashioned garden-of-maidens vibe, and the heavy focus on intricacies of school politics that seems so common to this genre
The Last Uniform - somewhat more comedic, but still a mostly old-fashioned story set in a girls' boarding school
Aoi Hana - I think this is a deliberate attempt to create a modern version of the genre, with more mature themes, but it mostly takes place in a Catholic girls' school
First Love Sisters - Don't remember this one that well, but I think it's basically a classic take on the genre
Fuwafuwa Futashika Yume Mitai - more modern, but it's about an all-girls school and that same sort of kouhai-sempai relationship
Gokujou Drops - Probably a lot more sex than is common to this genre (and a lot more comedic), but it's otherwise very similar
Holy Girl Paradigm - same here
A Kiss and a White Lily for Her - this one is kind of an anthology of different love stories between somewhat related characters set in a girls' boarding school
A Love Letter for the Marching Puppy - Set in some alternate history where the Imperial Japanese Army accepted women, so it's a cadet's school instead of a Catholic school, but other than that is basically 100% faithful to the genre
I imagine if you went back to yuri manga and novels from the 80s or 90s, you'd find a lot more that better meet your criteria, but I don't know much about that.