POST /api/v1/appointment expects { doctor_uuid, slot_start, slot_end,
note } with unix timestamps, and returns the appointment uuid at
data.uuid (not data.id). Send the right body, read the uuid, and on a
409 (slot already booked) alert the user and return to slot selection.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>