perf(backend): cut evaluate's DB round-trips; load the game in one query

EvaluatePlay (the hottest gameplay call, fired on every tile placement) now uses
the warm live-game cache directly: an active game stays cached (mutated in place
across moves, evicted only on finish), so the cached engine game and its immutable
seat list answer the membership check and the score with no DB read. The cold path
(eviction / first load) still loads and validates via the store. The seat list is
cached alongside the engine game for the membership fast path.

GetGame also folds its two round-trips (game, then seats) into one LEFT JOIN,
preserving the contract (same Game, a seatless game still returns empty seats, seat
order kept) — one round-trip for every remaining caller.

Measured at 500 players: evaluate p99 halves (200 -> 100 ms) and the per-op query
count drops. It does NOT cut postgres CPU — that is write-bound (per-move CommitMove
plus draft upserts and journal replays), the cheap indexed GetGame reads were never
its bottleneck, and postgres runs with headroom (~1.5 of 2 cores). So this is a
latency / query-volume optimization, not a DB-CPU one.

Regression cover: a non-player evaluate against a warm game asserts the cached-seat
membership path; the integration suite exercises GetGame's join across every game op.

backend/internal/game/service.go

@@ -287,12 +287,12 @@ func (svc *Service) Create(ctx context.Context, params CreateParams) (Game, erro
 	if err := svc.store.CreateGame(ctx, ins, seats, seeding.draws); err != nil {
 		return Game{}, err
 	}
-	svc.cache.put(id, g, params.Variant.String())
 	svc.metrics.recordStarted(ctx, params.Variant, params.VsAI)
 	created, err := svc.store.GetGame(ctx, id)
 	if err != nil {
 		return Game{}, err
 	}
+	svc.cache.put(id, g, params.Variant.String(), created.Seats)
 	// Honest-AI game seated with a robot: if the robot moves first, reply at once
 	// (the periodic driver is the fallback). No-op for every human-only game.
 	svc.triggerAI(created)
@@ -890,26 +890,35 @@ func (svc *Service) timeoutGame(ctx context.Context, gameID uuid.UUID, now time.
 // EvaluatePlay previews a tentative play for a seated player against the current
 // board without committing it: whether it is legal and what it would score.
 func (svc *Service) EvaluatePlay(ctx context.Context, gameID, accountID uuid.UUID, tiles []engine.TileRecord) (EvalResult, error) {
-	pre, err := svc.store.GetGame(ctx, gameID)
-	if err != nil {
-		return EvalResult{}, err
-	}
-	if _, ok := pre.seatOf(accountID); !ok {
-		return EvalResult{}, ErrNotAPlayer
-	}
-	if pre.Status == StatusFinished {
-		return EvalResult{}, ErrFinished
-	}
-
 	unlock := svc.locks.lock(gameID)
 	defer unlock()
-	g, err := svc.liveGame(ctx, pre)
-	if err != nil {
-		return EvalResult{}, err
+
+	// Hot path: an active game stays cached — the engine game is mutated in place across
+	// moves and evicted only when it finishes — so on a hit the cached live game and its
+	// immutable seat list answer the membership check and the score with no DB read. This
+	// preview is fired on every tile placement, the hottest gameplay call at scale.
+	g, seats, ok := svc.cache.get(gameID)
+	if !ok {
+		// Cold path: load and validate from the store, then replay into the cache.
+		pre, err := svc.store.GetGame(ctx, gameID)
+		if err != nil {
+			return EvalResult{}, err
+		}
+		if pre.Status == StatusFinished {
+			return EvalResult{}, ErrFinished
+		}
+		if g, err = svc.liveGame(ctx, pre); err != nil {
+			return EvalResult{}, err
+		}
+		seats = pre.Seats
 	}
+	if !seatedIn(seats, accountID) {
+		return EvalResult{}, ErrNotAPlayer
+	}
+
 	validateStart := time.Now()
 	rec, err := g.EvaluatePlay(tiles)
-	svc.metrics.recordValidate(ctx, pre.Variant, validateStart)
+	svc.metrics.recordValidate(ctx, g.Variant(), validateStart)
 	if err != nil {
 		if errors.Is(err, engine.ErrIllegalPlay) {
 			return EvalResult{Valid: false}, nil
@@ -1359,7 +1368,7 @@ func (svc *Service) ExportGCG(ctx context.Context, gameID uuid.UUID) (string, er
 // liveGame returns the live engine.Game for pre, rebuilding it from the journal
 // on a cache miss. Callers must hold the per-game lock.
 func (svc *Service) liveGame(ctx context.Context, pre Game) (*engine.Game, error) {
-	if g, ok := svc.cache.get(pre.ID); ok {
+	if g, _, ok := svc.cache.get(pre.ID); ok {
 		return g, nil
 	}
 	g, err := svc.replay(ctx, pre)
@@ -1374,7 +1383,7 @@ func (svc *Service) liveGame(ctx context.Context, pre Game) (*engine.Game, error
 		}
 	}
 	if !g.Over() {
-		svc.cache.put(pre.ID, g, pre.Variant.String())
+		svc.cache.put(pre.ID, g, pre.Variant.String(), pre.Seats)
 	}
 	return g, nil
 }