I want to think that the writers are throwing Sophie into scenes with Kate that are quite awkward on purpose? Like she doesn’t have a natural chemistry with her and it’s like they want it to be obvious that Kate is not into Sophie.

“Natural chemistry” is entirely subjective but the awkwardness in today’s scene was definitely on purpose. Sophie wasn’t even at the pub when Carla had her turn, there wasn’t any reason for her to show up at the hospital except for her to point out she’d caught on to Kate being distant and for Kate to lie to her about Carla being the only reason for it. At least for the moment, she’s still being kept at arm’s length.