Add lesson booking registration flow (offering, questions, policies)

Implements #3: students register for a private lesson by picking a slot,
answering the offering's intake questions, and accepting booking-scoped
policies. Payment is a clean seam for #7 (lessons land pending; payment_id
null; instructor confirms via PATCH /bookings/{id}/status).

- Schema: us_lessons += offering_id, recurrence, series_id, payment_id.
- Lesson: new fields + recurrence constants.
- BookingRepository::insertSeries() builds a weekly series sharing a
  series_id; AvailabilityRepository::findUnbookedInGroup() reserves a group.
- RegistrationGate (src/Registration/): validate + record intake answers and
  booking-scoped policy acceptances. Reused by group enrolment (#4).
- BookingEndpoint::book(): offering_id, recurrence, answers,
  accepted_policy_version_ids; single or weekly; records answers/acceptances
  (type lesson).
- GET /policies?scope=booking filter.
- Front-end booking.js: slot -> questions + policies -> submit.
- Wiring: RegistrationGate built in Plugin, passed via RestRegistrar.
- Test-only WP_Error stub in tests/bootstrap.php for gate testing.

Refs #3

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/Booking/Lesson.php

@@ -16,11 +16,25 @@ class Lesson {
 	 */
 	public const VALID_STATUSES = [ self::STATUS_PENDING, self::STATUS_CONFIRMED, self::STATUS_CANCELLED ];
 
+	public const RECURRENCE_SINGLE = 'single';
+	public const RECURRENCE_WEEKLY = 'weekly';
+
+	/**
+	 * All valid recurrence values.
+	 *
+	 * @var list<string>
+	 */
+	public const VALID_RECURRENCES = [ self::RECURRENCE_SINGLE, self::RECURRENCE_WEEKLY ];
+
 	public function __construct(
 		public readonly int $slotId,
 		public readonly int $studentId,
 		public readonly int $instructorId,
+		public readonly ?int $offeringId = null,
+		public readonly string $recurrence = self::RECURRENCE_SINGLE,
+		public readonly ?int $seriesId = null,
 		public readonly string $status = self::STATUS_PENDING,
+		public readonly ?int $paymentId = null,
 		public readonly ?string $notes = null,
 		public readonly ?int $id = null,
 	) {}
@@ -30,7 +44,11 @@ class Lesson {
 			slotId:       (int) $row->slot_id,
 			studentId:    (int) $row->student_id,
 			instructorId: (int) $row->instructor_id,
+			offeringId:   null !== $row->offering_id ? (int) $row->offering_id : null,
+			recurrence:   $row->recurrence,
+			seriesId:     null !== $row->series_id ? (int) $row->series_id : null,
 			status:       $row->status,
+			paymentId:    null !== $row->payment_id ? (int) $row->payment_id : null,
 			notes:        $row->notes,
 			id:           (int) $row->id,
 		);
@@ -45,9 +63,13 @@ class Lesson {
 		return [
 			'id'            => $this->id,
 			'slot_id'       => $this->slotId,
+			'offering_id'   => $this->offeringId,
 			'student_id'    => $this->studentId,
 			'instructor_id' => $this->instructorId,
+			'recurrence'    => $this->recurrence,
+			'series_id'     => $this->seriesId,
 			'status'        => $this->status,
+			'payment_id'    => $this->paymentId,
 			'notes'         => $this->notes,
 		];
 	}