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.

backend/internal/robot/driver.go

@@ -96,11 +96,20 @@ func (s *Service) maybeMove(ctx context.Context, rt game.RobotTurn, oppID uuid.U
 	return s.act(ctx, rt, now)
 }
 
-// maybeNudge sends a proactive nudge once the human has been idle past the
-// threshold. The social service enforces the once-per-hour-per-game limit and
-// rejects a nudge on the robot's own turn, so any such rejection is benign.
+// maybeNudge sends a proactive nudge on a lengthening, randomized schedule (proactiveNudgeGap):
+// the first lands ~60-90 min into the human's turn, and each one waits longer than the last, so a
+// long idle turn gets a handful of increasingly-spaced reminders rather than an hourly stream. The
+// gap is measured from the previous nudge (or the turn start for the first). The social service
+// still enforces the once-per-game floor and rejects a nudge on the robot's own turn, so any such
+// rejection is benign.
 func (s *Service) maybeNudge(ctx context.Context, rt game.RobotTurn, now time.Time) error {
-	if now.Sub(rt.TurnStartedAt) < proactiveNudgeIdle {
+	ref := rt.TurnStartedAt
+	if last, ok, err := s.social.LastNudgeAt(ctx, rt.GameID, rt.RobotID); err != nil {
+		return err
+	} else if ok && last.After(rt.TurnStartedAt) {
+		ref = last
+	}
+	if now.Sub(ref) < proactiveNudgeGap(ref.Sub(rt.TurnStartedAt), rt.Seed) {
 		return nil
 	}
 	if _, err := s.social.Nudge(ctx, rt.GameID, rt.RobotID); err != nil {