feat: add timeline API with schedule-aware enrollment aggregation

Implements POST /api/timeline endpoint that aggregates enrollment by
subject over 15-minute slots, filtering courses by their actual meeting
times. Includes ISR-style schedule cache with hourly background refresh
using stale-while-revalidate pattern, database indexes for efficient
queries, and frontend refactor to dynamically discover subjects from API.

migrations/20260131200000_timeline_indexes.sql

@@ -0,0 +1,13 @@
+-- Indexes for the timeline aggregation endpoint.
+-- The query buckets course_metrics by 15-minute intervals, joins to courses
+-- for subject, and aggregates enrollment. These indexes support efficient
+-- time-range scans and the join.
+
+-- Primary access pattern: scan course_metrics by timestamp range
+CREATE INDEX IF NOT EXISTS idx_course_metrics_timestamp
+    ON course_metrics (timestamp);
+
+-- Composite index for the DISTINCT ON (bucket, course_id) ordered by timestamp DESC
+-- to efficiently pick the latest metric per course per bucket.
+CREATE INDEX IF NOT EXISTS idx_course_metrics_course_timestamp
+    ON course_metrics (course_id, timestamp DESC);