Enter a tournament as a team you lead

Registers a team you lead directly into an OPEN-registration tournament and returns its participant ID. The entry is immediately APPROVED and consumes a participant slot, so the request is rejected with 409 error_tournament_full at capacity. Use the sibling apply endpoint for APPLICATION-mode tournaments - a mode mismatch answers 400 error_invalid_input rather than silently doing the other thing. Other refusals: 400 error_registration_closed outside the registration window, 400 error_roster_too_small below the tournament's teamSize, 409 error_already_entered when the team holds a non-terminal entry, and 403 error_competitive_banned while you are serving a competitive ban. There is no teamId body field - the acting team is the path segment, which is the only channel the leadership check covers. Requires the tournaments actor entry capability at read-write.