Yeah, it seems pretty clear that Amy is a huge influence on Peri right now.
It's pretty adorable.
Uuuugh!
That's why I don't want them in the barn, they belong in the temple!
Connie's great and all- I'd like to see more of her because she's super charming and her episodes are great despite being relatively rare-, but seeing as she goes to school and has a normal human life beyond Steven it doesn't make much sense for her to show up a lot...unlike Lapis and Peridot who have no where to be in particular, are gems who know about gem stuff that even the OG CGs might not know about, have very useful powers/skills, and also have a huge personal steak in two of the major plot points.
Hopefully the barn is temporary.
you have to look at it this way.
during the major plot points they will likely be around, as you said they have a vested interest in those, but during the lighter less major story focused episodes are they really needed?
the show only runs 11 minutes. you already typically have the 4 main characters in the episodes, the simple fact is that those characters alone can typically fill up the 11 minutes the show is. adding two more characters can result in good things, but at the same time it can easily result in being just to much of a good thing and having the episode fall flat. We have already know of one time peridot was originally planned to have more of a presence in a episode but then was cut just because they couldn't fit everything with her there as well.
beyond all of that it's not like voice actor/actresses are free. Getting a large cast each episode tends to cost more money. once we get back to the main plot I am sure they will show up again, but I wouldn't be surprised if we got 5-10 more episode of the week type things going on here and if they only showed up once or twice during them.