The Eminence in Shadow got Anime adaptation because of the Light Novel and not Manga version. The reason why you see there are differences between Anime and Manga because it cover mostly from Light Novel. So far, the season is up to Volume 3. From Volume 4 and onwards, the Light Novel will differ from it's Web Novel version. In LN, Cid was adaptational heroism where he maintains his idiot hero persona while in WN, his actions during the Great Trading Company received many criticisms from Readers. Thus, it is unsure which Direction, Manga will take on. Latest Volume is 7 in Japan. I read up to Vol 6 (Jack Ripper Arc).
I've watched the anime before reading this and there seem to be some changes from the anime.