feat(chat): unread read-receipts with lobby/game dot and history-open ack

Persist per-message read state as a chat_messages.unread_seats bitmask
(migration 00008): a text message seeds every recipient seat's bit, a nudge
only the awaited seat's. A seat's bit clears when the player opens the move
history or chat (POST /games/:id/chat/read, sent only when something is
unread), and a nudge additionally clears when its recipient answers by moving
(a wired game NudgeClearer, dependency-inverted so game keeps off social).

UI shows a per-viewer unread dot in the lobby (next to the opponent) and the
game score bar — the unread_chat game-view flag seeds it from authoritative
REST views, live chat/nudge events raise it. Opening the move history counts
as reading (even without entering chat): the 💬 fade-blinks twice and the
client acks. Admin Messages gains an unread-only filter, a read/unread column,
and a per-message card with the per-seat read breakdown. Observability:
chat_read_duration histogram + chat_unread_messages gauge + social tracing.

backend/internal/game/service.go

@@ -45,8 +45,12 @@ type Service struct {
 	// its asynchronous TriggerMove); nil disables the fast path (the scan still covers
 	// these games). Kept as a func so the game package never imports the robot package.
 	aiTrigger func(gameID uuid.UUID)
-	metrics   *gameMetrics
-	log       *zap.Logger
+	// clearNudges, when set, marks the actor's pending nudges in a game read once they
+	// have committed a move (a nudge answered by moving stops counting as unread). It is
+	// best-effort and kept as a func so the game package never imports the social package.
+	clearNudges func(ctx context.Context, gameID, accountID uuid.UUID) error
+	metrics     *gameMetrics
+	log         *zap.Logger
 }
 
 // NewService constructs a Service. store and accounts wrap the same pool;
@@ -89,6 +93,14 @@ func (svc *Service) SetAITrigger(trigger func(gameID uuid.UUID)) {
 	svc.aiTrigger = trigger
 }
 
+// SetNudgeClearer installs the hook that marks a mover's pending nudges read after
+// their move commits. It must be called during startup wiring; the default (nil)
+// leaves nudges to be cleared only when the recipient opens the move history or chat.
+// The social package wires its ClearNudges here.
+func (svc *Service) SetNudgeClearer(fn func(ctx context.Context, gameID, accountID uuid.UUID) error) {
+	svc.clearNudges = fn
+}
+
 // triggerAI fires the honest-AI fast-move hook for an active vs_ai game (best-effort,
 // fire-and-forget). It is a no-op for non-AI games, finished games and when no hook is
 // installed, so callers can invoke it unconditionally after a create or commit.
@@ -567,6 +579,13 @@ func (svc *Service) transition(ctx context.Context, gameID, accountID uuid.UUID,
 		return MoveResult{}, err
 	}
 	svc.afterCommitDrafts(ctx, gameID, accountID, rec)
+	// A nudge the actor answered by moving stops counting as unread (best-effort; the
+	// move has committed, so a cleanup failure is logged, not surfaced).
+	if svc.clearNudges != nil {
+		if err := svc.clearNudges(ctx, gameID, accountID); err != nil {
+			svc.log.Warn("clear nudges after move", zap.Error(err))
+		}
+	}
 	// Record the seat's think time (turn start to commit) for the move-duration
 	// metric; the timeout path commits separately and is excluded by design.
 	svc.metrics.recordMoveDuration(ctx, pre.Variant, post.MoveCount, svc.clock().Sub(pre.TurnStartedAt))