[rooms] record invention room usage

apps/rooms/migrations/0023_room_invention.sql

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+-- Which inventions a room has in it — one row per (room, invention).
+--
+-- Generated from packages/domain/src/rooms-db.ts (SUBROOM_SCHEMA_DDL) — keep in sync.
+--
+-- A room save (`POST /rooms/:id/subrooms/:sid/data`) carries `InventionUsage`, a base64
+-- protobuf listing the inventions in the saved scene (see `decodeInventionUsage`). Each
+-- save re-derives the room's rows here from every one of its subrooms, so the table is the
+-- union across the room and an invention removed from it drops out on the next save.
+--
+-- Empty until rooms are next saved: the `InventionUsage` already stored on subrooms is not
+-- backfilled, since decoding it is not something SQL can do.
+
+CREATE TABLE IF NOT EXISTS room_invention (
+  room_id INTEGER NOT NULL,
+  invention_id INTEGER NOT NULL,
+  PRIMARY KEY (room_id, invention_id)
+);
+
+-- The reverse lookup: which rooms use this invention.
+CREATE INDEX IF NOT EXISTS idx_room_invention_invention ON room_invention (invention_id);