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/social/social.go

@@ -13,11 +13,16 @@ import (
 	"time"
 
 	"github.com/google/uuid"
+	"go.opentelemetry.io/otel"
+	"go.opentelemetry.io/otel/trace"
 
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/notify"
 )
 
+// tracerName scopes the social domain's OpenTelemetry spans.
+const tracerName = "scrabble/backend/social"
+
 // GameReader is the slice of the game domain the social package needs: the seated
 // accounts in seat order, the seat index whose turn it is, and the game status, plus
 // a shared-game test. game.Service satisfies it, so chat, nudge and the
@@ -71,6 +76,8 @@ var (
 	ErrFriendCodeInvalid = errors.New("social: friend code is invalid or expired")
 	// ErrNotParticipant is returned when an account is not seated in the game.
 	ErrNotParticipant = errors.New("social: account is not a player in this game")
+	// ErrMessageNotFound is returned when an admin message lookup finds no such message.
+	ErrMessageNotFound = errors.New("social: message not found")
 	// ErrChatBlocked is returned when the sender has disabled chat for themselves.
 	ErrChatBlocked = errors.New("social: chat is disabled for this account")
 	// ErrMessageTooLong is returned when a chat message exceeds the rune limit.
@@ -104,6 +111,7 @@ type Service struct {
 	games    GameReader
 	pub      notify.Publisher
 	metrics  *socialMetrics
+	tracer   trace.Tracer
 	now      func() time.Time
 }
 
@@ -116,6 +124,7 @@ func NewService(store *Store, accounts *account.Store, games GameReader) *Servic
 		games:    games,
 		pub:      notify.Nop{},
 		metrics:  defaultSocialMetrics(),
+		tracer:   otel.Tracer(tracerName),
 		now:      func() time.Time { return time.Now().UTC() },
 	}
 }