FEAT: Video Search In Discovery

discovery/internal/db/migrations/0005_add_video_recency_index.up.sql

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+-- Browsing the catalogue, and paging through it.
+--
+-- Every search orders by (rank, created_at, id). When there is no title term
+-- the rank is a constant, and Postgres folds a constant sort key away — so the
+-- order that remains is exactly this index, and a browse becomes an index-only
+-- scan that stops as soon as the page is full instead of sorting the table.
+--
+-- Measured at 200k rows: a first page of a browse goes from a 15 ms parallel
+-- sequential scan with a top-N sort to 0.03 ms. It matters more for the cursor
+-- than for the first page — the keyset comparison (created_at, id) < (…)
+-- becomes an index condition rather than a filter, so a deep page is a seek
+-- to the right place in the index rather than a walk through everything
+-- before it.
+--
+-- DESC on both columns to match the ORDER BY: a btree can be read backwards,
+-- but only as a whole, so a mixed-direction ordering could not use it.
+CREATE INDEX videos_recent_idx ON videos (created_at DESC, id DESC);