High School Prodigies Have It Easy Even In Another World! is a terrible, no-good, horrible, very bad, utterly trashy anime.
Prodigies is also fully self-aware that it is trash… and doesn’t care. Prodigies just goes ahead and has fun doing what it’s doing on Prodigies’ own terms anyway. So Prodigies ends up being kind of fun if you can accept that and just run with it.
In terms of premise, well, I’m not sure that there’s much I can add to the formal title from the light novel series. You have a series of high school prodigies who wind up in another world and proceed to completely change it. Because they’re just that good.
The show is heavy on the fanservice, to the point where it will be a dealbreaker for many. In this respect Prodigies strays into some uncomfortable territory, and does so for little more than prurience (I don’t want to go into too much detail here, but content warnings are applicable).
Prodigies also has one episode where the doctor commits ethical violations on a truly epic level. Hippocratic Oath? Oh, that’s more of a guideline, right? And yet she’s regarded as one of the righteous for doing so. So that’s more than a little problematic.
That said, Prodigies is mostly trashy fun that couldn’t possibly work as smoothly as it does, but gets away with it by being so self-aware that it is trash and not caring. I enjoyed it on that level, but won’t ever be likely to rewatch it.
Here’s the OP (note the fanfares which do rather set the tone of the series nicely)
* AKA Chōjin-Kokoseitachi wa Isekai demo Yoyu de Ikinuku Yōdesu! per Wikipedia.