[api] fix slow rooms badge query

packages/domain/src/rooms-db.ts

@@ -2846,17 +2846,31 @@ async function hydrateRooms(db: D1Database, rooms: Room[]): Promise<Room[]> {
 	return rooms
 }
 
+/**
+ * Whether `custom_avatar_item` has been seen on this database. API owns that table's migration
+ * and room deployments can precede it, so {@link attachBadges} probes for it — but a table
+ * never goes away once created, so a hit is remembered and the probe (a scan of
+ * `sqlite_master`, on every room page) runs only until the first hit.
+ */
+let badgeTableSeen = false
+
 /** Published room-linked image badges; drafts remain on the creator's Studio shelf. */
 async function attachBadges(db: D1Database, rooms: Room[]): Promise<void> {
 	if (!rooms.length) return
-	// API owns this table's migration; room deployments can precede that migration.
-	const exists = await db
-		.prepare("SELECT 1 FROM sqlite_master WHERE type='table' AND name='custom_avatar_item'")
-		.first()
-	if (!exists) {
-		for (const room of rooms) room.Badges = []
-		return
+	if (!badgeTableSeen) {
+		const exists = await db
+			.prepare("SELECT 1 FROM sqlite_master WHERE type='table' AND name='custom_avatar_item'")
+			.first()
+		if (!exists) {
+			for (const room of rooms) room.Badges = []
+			return
+		}
+		badgeTableSeen = true
 	}
+	// Served by `idx_custom_avatar_item_badge_room` (api migrations/0035), a PARTIAL index over
+	// `outfit_type = 1000` keyed by the `json_extract(data,'$.CustomBadgeMetadata.RoomId')`
+	// expression. SQLite matches both only as written: drop or rephrase either term and this
+	// goes back to scanning every custom avatar item on every room page.
 	const rows = await db
 		.prepare(
 			"SELECT data,json_extract(data,'$.CustomBadgeMetadata.RoomId') AS room_id FROM custom_avatar_item WHERE outfit_type=1000 AND accessibility<>0 AND json_array_length(json_extract(data,'$.CurrentSaves'))>0 AND json_extract(data,'$.CustomBadgeMetadata.RoomId') IN (SELECT value FROM json_each(?))"