Granblue fantasy

Even without delving into my vast list of watched content, the first thing that comes to mind is Rokudenashi Majutsu Koushi to Akashic Records. But whether the school is ultimately magical or not is irrelevant, in the sense that thematically it could be something like "superpowers" instead of magic, but the pattern remains the same; only the overall theme changes.

I don't accept this example for two reasons, or rather, one:
1) I immediately see that the characters here are not dressed as is customary in decent English schools for wealthy or aristocratic children, meaning I immediately have a serious (and, I'm sure, justified) doubt that this particular school actually has anything to do with what I was talking about.
2) "Alzano" is a word that clearly does not associate with British culture, unlike "Manaria," which is generally compatible with it. This basically says the same thing.
And yes, if we're talking about magical schools, specifically English-style schools, then of course it's important that it's actually a magical school...

And it doesn't matter who might have set certain trends. Well, let's say pointed hats from this British writer became popular in pop culture, so what?
If I understand correctly, Tolkien popularized the image of orcs as they are today, but how many people think of him when they encounter this race in any work? I, for example, didn't remember him until this conversation, although there is more than enough content with orcs these days. If you see a compass or paper somewhere, do you immediately think of Chinese culture? Why not, it originated there. These are all borrowed technological and cultural elements. A Japanese school, for example, will not become European just because they wear clothes that are not traditional for that country. Oh, wait, even the Japanese sailor uniform was created based on a European form. So what does that mean...? Is it Japanese or European? Obviously, if we're talking about Japan or content created by Japanese people, then it's Japanese.

I almost agree with this, with reservations. The original source can be important if its strong influence on the subject being discussed still exists. That is, you are right about the examples of paper and the compass, but a hypothetical Gothic cathedral will still remind you of Western Catholic culture, even if it is built somewhere in the Philippines. I can give an example even closer to your worldview – a European wearing a kimono is still wearing an item of Japanese culture and is most likely doing so not just for fun, but because they need it for cosplay/masquerade/performance, or as a sign of solidarity with Japanese traditions (as in the film "The Last Samurai"). That is, content sometimes matters and is preserved.
In summary, your reasoning applies only to those items that have been culturally borrowed firmly and for a long time, which, in my opinion, still does not apply to English sweaters with badges and plaid skirts...

If one character calls another character "senpai" in a setting that thematically resembles European culture, it still doesn't mean that it's okay to write the name in the translation, because this violates the character that the author has given to the characters and the level of relationship between them. Just as in Japan, no one throws around phrases like "I love you" (aishiteru) left and right; instead, less serious options like "suki" and "daisuki" are used, which can refer to both friendship and romantic relationships, and if you still translate it as "I love you," the original meaning is lost, but the localizers don't care; they just want to write it the way it's customary to speak in the English-speaking community. Localization is a degenerative practice of LiTeRaLi orcs. Then people consume such low-quality translations, and even in dubs, and never understand the nuances of what they see and hear, continuing to perceive onigiri as a donut.

“Senpai” is a very nuanced word, and yes, seeing it in the original, I would almost certainly transfer it into the translation. But again, my point is that it's better for the author and translator to agree, because in this specific example, using even the same "senpai" may turn out to be a minor detail, the presence of which was more influenced by the author's linguistic traditions than they intentionally decided so.

I was also thinking that you might not know what I'm referring to when I say that the author can give recommendations for correct translation, so I'm giving a link to what I think is a standard for this, which immediately answers all questions about how and what to translate, and whether it should be done:
http://www.tolkien.ro/text/JRR%20Tolkien%20-%20Guide%20to%20the%20Names%20in%20The%20Lord%20of%20the%20Rings.pdf