Boston should see Bieber, Plesac and Allen this weekend, so my guess is that Battenfield already made his last start for the foreseeable future (although he was good in his first two starts). By the start of next week, Sam Hentges should be back from the IL which eliminates any opportunities for Battenfield or Konnor Pilkington in the pen, so they return to the AAA rotation with Allen and Bibee continuing to see what they can do in the rotation.
Battenfield, Pilkington, Gaddis and Curry had gotten the opportunities to fill in for injuries up until this week, but those are the guys with the lowest ceilings on the 40-man roster. I wouldn't be surprised to see a couple of them make a successful transition to the bullpen (see: Eli Morgan), but Cody Morris should also be healthy by summertime and I'd be surprised if we don't see Gavin Williams sometime this season. Williams doesn't need to be on the 40-man roster until they're certain he's ready to join the MLB rotation though.
Cleveland often acts as both a buyer and a seller at the trade deadline, and they have so many starters and middle infielders at AAA that they almost have to deal a couple of those guys or one or two of Zach Plesac, Cal Quantrill or Amed Rosario. They'll also want to keep some healthy competition though, because Shane Bieber most likely gets traded prior to his walk year in 2024.