In terms of joining Phase it's usually been some variation of either Clara personally asked and wanted to be in JP, or the only spot fishman had left was a JP spot so he put her there. (funny enough I think I've heard Clara say both versions on stream). Being in EN didn't seem to be on the table at any point.
About joining the basement a month after her genmates, is a little more interesting. Clara showed those discord requests from sakana; it looked like the earliest was 6/29. Beryl graduated on 6/26, so it's safe to assume she already established a working relationship with the fish at some point prior. Hitori, (we've agreed that it's Loki, yes?) fellow corpo mate, graduated 2 weeks prior to Beryl. Two talents from the same company, leaving within the same month, but fish accepted one talent an entire month before the second one? Not just Loki, but the other 3 as well before Clara? So maybe the rrat is Fishman took longer to decide what to do with Beryl then anybody else. (Gen 3 included?) And going by Airi's interview, sakana doesn't let the talent into the basement until they're "finalized".