The anime has horrible pacing. The manga's story pacing is great and much closer to the real story in the light novel. I think what makes you feel that way is how slowly it gets updated, how the chapters are only being drip-fed to us, and how fast the anime rushes through everything.
Edit: Also, After the Rain adapts bonus short story chapters from the light novel, all of which were completely skipped in the anime. That's all you need to know, really xD
Yeah, anime really just does a speed run, skipping over way too much stuff. Had it gone at a pace of maybe 2 volumes per season, they could fit in more detail and skip less.
Anime skipping V5.5 kinda hurts, since that volume gives backstory to the main side characters, and their backstories aren't exactly happy ones, which helps us understand them better. Like with Itsuki and Chitose, what you see in the anime is a 180 from who they were before. With Mahiru, we get a valuable backstory that explains why she's so aggressive in her attempts to court Amane.
On a simpler note, this chapter is just more sugar being poured onto us. Too much cuteness to contend with