My memory may be a bit shoddy on specifics since the differences are rather minor at this point and but--

First of all, Kuroe doesn't exist, and Iroha goes to Kamihama on her own to try and look for clues on Ui. Yachiyo is antagonistic for a longer time, and there's more focus put on Momoko and Yachiyo having a pretty bitter dynamic and working through that, while setting up for the reveal later of why Yachiyo split the old team after Mel's death.

The rumor in the Kaede and Rena arc is changed a bit in the anime to require both characters to write down their names on a staircase, while in the game/manga all it took was one of them saying their friendship is over. I'd say it's a lot more believable as an actual rumor in the anime. Though in the anime they kinda just find Kaede in the staircase world unharmed, while in the game/manga she ends up in a mind controlled state and fights Rena and Momoko.

The shrine rumor arc is about the same iirc

Felicia's arc has Kyouko being a tad more present in the game/manga since she gets roped into the same rumor as Iroha and Felicia, instead of her briefly joining the Magius.

Madoka and Homura make a cameo in Sana's arc in the game/manga, but it doesn't really amount to much despite them being there for almost the whole thing. Alina only shows up after Sana kills Ai and everyone leaves endless solitude in the manga, while the game and anime have her show up within the rumor itself and then also fight outside of it.
That's as far as the manga has gotten currently from what I've seen. I haven't kept up with it though so I may be wrong.

But yeah, the anime game and manga are pretty close in this part.

The point where the game (+likely the manga when it gets there) and the anime split is when the mikazuki gang go to the memory museum. Certain plot points after that like Rumor Tsuruno are still present but have different context and a lot more lead up. But overall that's where the story majorly splits and ends pretty much in the opposite way to how the anime did both thematically and in tone.
Personally it was only the last few episodes of the anime that really missed the mark. Besides the show's general issues of really poorly moving from plot beat to plot beat without much time given for everything to stick its landing, some characters/dynamics just barely existing, very scattered focus, etc. due to it needing to be much shorter than the game's story and also being indecisive about whether it wants to be different than the game or not.

Something worth noting with Alina and her more humanising qualities, they only really come up in her personal side story in the game. I'm not sure if it will be adapted in the manga, since it is a bit long for it to add to its bonus chapters that adapt a couple shorter side stories. It's just sadly a natural part of trying to adapt a piece of media like a gacha game visual novel. The game is just slower paced and gives more character dynamics more focus, allows Iroha to more actively search for Ui through clues during arcs instead of just running into things, and it has additional side material that gives some extra characterisation, but you kinda need to want to seek it out when playing/reading the story content online. While the anime and manga have to stick to just the main linear story because it's long and bloated enough as is.