Stage 17: fix the robot-nudge frequency + per-game push language

Two owner-reported defects from a live contour game.

A. Frequency: the robot's proactive nudge fired hourly for 12h+ (a 12h idle threshold
   then the 1h cooldown, uncapped). Replaced with a lengthening, randomized schedule
   (proactiveNudgeGap): the first nudge ~60-90 min into the human's turn, each later gap
   growing toward 1-6h (uniform sample in [60min, ceil], ceil ramping 90min->6h over 12h
   of idle, measured from the previous nudge), so a long wait gets a handful of
   increasingly-spaced reminders instead of a stream.

B. Language: out-of-app push routed by the recipient's GLOBAL service_language
   (last-login-wins), so after re-logging via the RU bot an English game's nudges came
   from the RU bot. Now a game push (your_turn, game_over, nudge, match_found) carries
   the game's own language (engine.Variant.Language) on push.Event, and the gateway
   routes by it (falling back to service_language for non-game pushes). The New-Game
   variant-gating guarantees the game's bot is one the player has started, so delivery is
   never blocked.

Tests: proactiveNudgeGap unit + retimed TestRobotProactiveNudge; TestVariantLanguage;
emit your_turn/game_over language; TestNudgeRoutedByGameLanguage integration. Docs:
ARCHITECTURE (§7 nudge, §10/§13 routing), FUNCTIONAL (+ _ru), PLAN tracker.

gateway/cmd/gateway/main.go

@@ -214,7 +214,7 @@ func runPushPump(ctx context.Context, backend *backendclient.Client, hub *push.H
 			// deliver the event over the platform push channel. Done in a goroutine
 			// so a slow connector never stalls the in-app firehose.
 			if conn != nil && connector.OutOfAppKind(ev.GetKind()) && !hub.HasSubscribers(ev.GetUserId()) {
-				go deliverOutOfApp(ctx, backend, conn, ev.GetUserId(), ev.GetKind(), ev.GetPayload(), logger)
+				go deliverOutOfApp(ctx, backend, conn, ev.GetUserId(), ev.GetKind(), ev.GetPayload(), ev.GetLanguage(), logger)
 			}
 		}
 		if !sleep(ctx, pushReconnectDelay) {
@@ -227,7 +227,7 @@ func runPushPump(ctx context.Context, backend *backendclient.Client, hub *push.H
 // Telegram identity and have not confined notifications to the app, asks the
 // connector to deliver the event. It is best-effort: every failure is logged and
 // dropped (the in-app stream remains the primary channel).
-func deliverOutOfApp(ctx context.Context, backend *backendclient.Client, conn *connector.Client, userID, kind string, payload []byte, logger *zap.Logger) {
+func deliverOutOfApp(ctx context.Context, backend *backendclient.Client, conn *connector.Client, userID, kind string, payload []byte, gameLang string, logger *zap.Logger) {
 	target, err := backend.PushTarget(ctx, userID)
 	if err != nil {
 		logger.Warn("push target lookup failed", zap.String("user_id", userID), zap.Error(err))
@@ -236,7 +236,13 @@ func deliverOutOfApp(ctx context.Context, backend *backendclient.Client, conn *c
 	if !connector.DeliverToTarget(target.ExternalID, target.NotificationsInAppOnly) {
 		return
 	}
-	if _, err := conn.Notify(ctx, target.ExternalID, kind, payload, target.Language); err != nil {
+	// A game event carries its own language, so the push comes from the game's bot rather than
+	// the recipient's last-login bot (Stage 17); other events fall back to the service language.
+	lang := target.Language
+	if gameLang != "" {
+		lang = gameLang
+	}
+	if _, err := conn.Notify(ctx, target.ExternalID, kind, payload, lang); err != nil {
 		logger.Warn("out-of-app notify failed", zap.String("kind", kind), zap.Error(err))
 	}
 }