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]>

assets/css/frontend.css

@@ -117,6 +117,36 @@
     color: #8a6d1a;
 }
 
+.us-type-filter {
+    display: flex;
+    flex-wrap: wrap;
+    align-items: center;
+    gap: 8px 16px;
+    margin-bottom: 12px;
+    padding: 8px 12px;
+    border: 1px solid #eee;
+    border-radius: 4px;
+}
+
+.us-type-filter-heading {
+    font-weight: 600;
+}
+
+.us-type-filter-choice {
+    display: inline-flex;
+    align-items: center;
+    gap: 6px;
+}
+
+.us-type-filter-clear {
+    margin-left: auto;
+    padding: 4px 12px;
+    border: 1px solid #ccc;
+    border-radius: 4px;
+    background: transparent;
+    cursor: pointer;
+}
+
 .us-view-toggle {
     display: flex;
     gap: 8px;