Yes, but for some reason it seems to perform worse there.

Perhaps whatever algorithms Cursor uses to prepare the context it feeds the model are a good fit for Claude but not so much for the others (?). It's a random guess, but whatever the reason, there's a weird worsening of performance vs pure chat.

Yes but every model besides claude-3.5-sonnet sucks in Cursor, for whatever reason. They might as well not even offer the other models. The other models, even "smarter" models, perform vastly poorer or don't support agent capability or both.