Email-first login probe. Returns route "otp" with challenge timestamps when the email is the representative of a claimable child account, and route "password" for everything else — an existing user, an unknown email, or an email with nothing to claim. Registered and unknown emails are indistinguishable in the response. One case answers 422 instead: an email representing more than one claimable organization cannot be claimed self-service and is directed to support.