Filter booking calendar slots by available lesson type

Not every open time can be booked as every private-lesson type: a slot tied
to an offering takes that offering only, and a generic slot only takes types
whose length fits. Students had no way to see that before clicking a time.

The booking calendar now carries a lesson-type filter — a checkbox per active
private-lesson type, fetched once from GET /offerings?kind=private_lesson.
Ticking types narrows the calendar to the times bookable as one of them and
re-anchors the week view on the earliest match. The registration form's
Lesson type picker is narrowed the same way, and a lone remaining type is
pre-selected with its intake questions loaded.

Bookability is decided by offeringFitsSlot(), the client-side mirror of the
rule POST /bookings enforces; the filter is a browsing aid and the server
still validates every booking. No ticks means no filter, and the whole
control is hidden when the studio offers fewer than two private-lesson types.

Closes #117

Co-Authored-By: Claude Opus 5 <[email protected]>

docs/features/lesson-booking.md

@@ -20,8 +20,8 @@ Students register for a private lesson by choosing an offering, picking a time (
 | `created_at`   | DATETIME         | Insertion time                                             |
 
 ## Registration Flow
-1. Student opens the page with the `[us_booking]` shortcode and browses open slots as a weekly calendar (the default, anchored to the week of the earliest open slot) or an agenda list (view toggle with previous/next-week navigation; times shown in 12-hour AM/PM form).
-2. Student picks a slot and an **offering** (a 30 or 60-minute private-lesson type). When the slot is tied to an offering the form shows it locked (the student sees exactly what they are booking); otherwise the form presents the instructor's active private-lesson offerings whose duration fits the slot. Every booking requires an offering — a generic slot with no fitting offering cannot be booked online.
+1. Student opens the page with the `[us_booking]` shortcode and browses open slots as a weekly calendar (the default, anchored to the week of the earliest open slot) or an agenda list (view toggle with previous/next-week navigation; times shown in 12-hour AM/PM form). A **lesson-type filter** above the calendar narrows the open times to those bookable as the chosen types (see **Lesson-Type Filter**).
+2. Student picks a slot and an **offering** (a 30 or 60-minute private-lesson type). When the slot is tied to an offering the form shows it locked (the student sees exactly what they are booking); otherwise the form presents the instructor's active private-lesson offerings whose duration fits the slot, narrowed to the filtered types. When exactly one type remains it is pre-selected (its intake questions load immediately). Every booking requires an offering — a generic slot with no fitting offering cannot be booked online.
 3. For a `weekly` reservation, the same weekday/time is held for the rest of the offering's term.
 4. Student answers the offering's questions (`GET /offerings/{id}/questions`).
 5. Student accepts the current published policy versions (`GET /policies`) — required to continue.
@@ -31,6 +31,28 @@ Students register for a private lesson by choosing an offering, picking a time (
 9. Instructor sees the booking under **My Lessons** and may update status via `PATCH /bookings/{id}/status`.
 10. The booking page also shows the student their upcoming lessons (`GET /bookings`) — each with the booked offering's name and length, when it happens, a per-lesson status badge (pending payment / confirmed), and a **Cancel** button. Only the soonest five are shown; a **Show all** control reveals the rest. `GET /bookings` includes `offering_title` and `duration_minutes` for each lesson so the list needs no extra request.
 
+## Lesson-Type Filter
+Not every open slot can be booked as every private-lesson type — a slot tied to
+an offering takes that offering only, and a generic slot only takes types whose
+length fits. The booking calendar therefore carries a lesson-type filter above
+the view toggle: a checkbox per active private-lesson type (from
+`GET /offerings?kind=private_lesson`, fetched once per page load), showing the
+instructor's name alongside the title when the catalog spans more than one
+instructor. The filter is hidden when there is only one bookable type.
+
+Ticking one or more types narrows the calendar to the slots bookable as one of
+them; no ticks means no filter. Picking a filtered slot narrows the registration
+form's **Lesson type** picker the same way, and when exactly one type remains it
+is pre-selected and its intake questions load immediately. Changing the filter
+re-anchors the week view on the earliest matching slot, so the student never
+lands on an empty week. **Show all types** clears the filter.
+
+Bookability is decided client-side by `offeringFitsSlot()` in
+`assets/js/booking.js` — the mirror of the rule `POST /bookings` enforces (same
+instructor, the tied offering when there is one, otherwise a matching
+`duration_minutes`). The filter is a browsing aid only: the server re-checks
+every booking regardless.
+
 ## Cancellation
 Students cancel their own lessons via `POST /bookings/{id}/cancel` (idempotent).
 Cancelling marks the lesson `cancelled`, frees the availability slot for