You’re right, and this is a known limitation we’re tracking. Right now the repository picker in the iOS app only lists repositories from connected providers like GitHub, GitLab, Bitbucket, and Azure DevOps. Repositories that live natively in Origin aren’t included yet, so there’s no way to pick one from inside the app at the moment. (Origin repos that are mirrored from GitHub still show up, because they come through your GitHub connection.)
In the meantime, the easiest way to start an agent on your Origin repo from your phone is to open cursor.com/agents in your mobile browser, pick the Origin repository there, and send your task. Once the agent is running it will appear in the iOS app, and you can follow it and reply from there.
I can’t share an ETA yet, but I’ll update this thread when it ships.