The first episode was IMO rather good, and stayed well within the expected from the manga. The whole shtick was Claire bullying Rei and Rei going "bully me more!", it might sound silly but it's fun.
the story has grown on me. Glad to hear the anime starting off on a good note.
Ditto. The obsession of Rei over Claire is a bit weird, but once you brush it off as "otaku fan doing otaku fan things", the story gets in the right spot between slapstick comedy and serious drama.
As OP put it: Isekai "bully me more!" from an actual know-it-all player. I agree with Rae's point about Claire's considerations, and am intrigued to see this line toed further.