First of all it's nothing like manga. Completly different events happening. The way the anime shows the story is too serious in a way you can believe he was just an ordinary kid who had 8th grade syndrome and they completly ignored the humor aspect that happened in the manga. They also seem like they skipped the half of the manga in which considering how it started it seem like it's about a different story that's not like manga at all.
Whoever did the adaptation clearly didn't even read the manga. They just read what's this about and learned who is the main characters and that's it. It's like spin-off at this point. Paralel universe story. A remake. It's not like they made the anime of the manga, they just used the idea but they changed it into whatever they wanted.
TBH if I had first watched this anime I wouldn't give manga a chance so I couldn't know how great the manga is which it made me realize when I dislike an anime I should try their manga.
In detail, Shadow's character is not so similar as the manga Shadow. In manga he makes fun of the situation, in this anime he is like he seriously has 8th grade syndrome. He doesn't look cool at all. Manga Shadow is cool but in anime he is just some ordinary edgy kiddo. Also manga Shadow looks like older teen but anime Shadow looks like a kid LOL. Manga drawings really top-notch on showing what kind of people they are but anime drawing is fan level LOL. Also Shadow's voice is generic male kiddo voice which made me cringed. He can't even play Moonlight Sonata straight.
I have no idea why they changed the beginning of the manga so much and skipped into far future. We really didn't have to watch some random girl's substory. We also didn't need over-pornographic scenes of that girl just from the first seconds of the anime. If it wasn't about The Eminence in Shadow I would just stop watching it after 2 minues, it's that bad. So yeah it's even bad as an anime.
The way anime shows the story is nothing more than generic serious harem-anime that revolves around a kid who have 8th grade syndrome but manga ain't like that at all. I have no idea why they didn't actually turned manga into anime. Thus it's just utter rubbish, nothing more nothing less. Read the manga it's the real The Eminence in Shadow.