They used it to create potions and spells that are equivalent to the medical industry, as well as the beauty industry, sports, frivolous things like that.

It's implied serious research goes on, but never really shown.

There's also wizard versions of cops, and government officials, naturally.

Magical knowledge replaces engineering and math as well. A civil engineer's building design equivalent would be a series of complicated spells put on a small building to make it a massive one inside.

Also in the books, Hogwarts was really only secret to the muggles, every wizard in Britain knows where it is.

But imagine all the high schoolers who complain "why do I need to learn algebra, I won't even need it in [job]. It's like that. Some won't need it, but it's still a useful skill.

Lol I don't think it's ever really explained beyond "improve the lives of secret magic people." But I think a common trope of a lot of fantasy media with mages is that they get so caught up in the magic, they tend to ignore everything else going on around them, which often leads to either a clash with non-magic people, or a reluctant alliance.

Ivy league College in a nutshell

Haven't read the books either, but I have seen some of the movies.

Basically everything in the Wizarding world is done with magic. Travel, communication, cooking, dishes, the lot. You can't even enter the world without either magical knowledge or someone showing you how, even Harry Potter himself needed someone to guide him through.