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/postgres/jet/backend/model/chat_messages.go

@@ -13,11 +13,12 @@ import (
 )
 
 type ChatMessages struct {
-	MessageID uuid.UUID `sql:"primary_key"`
-	GameID    uuid.UUID
-	SenderID  uuid.UUID
-	Kind      string
-	Body      string
-	SenderIP  *string
-	CreatedAt time.Time
+	MessageID   uuid.UUID `sql:"primary_key"`
+	GameID      uuid.UUID
+	SenderID    uuid.UUID
+	Kind        string
+	Body        string
+	SenderIP    *string
+	CreatedAt   time.Time
+	UnreadSeats int16
 }

backend/internal/postgres/jet/backend/table/chat_messages.go

@@ -17,13 +17,14 @@ type chatMessagesTable struct {
 	postgres.Table
 
 	// Columns
-	MessageID postgres.ColumnString
-	GameID    postgres.ColumnString
-	SenderID  postgres.ColumnString
-	Kind      postgres.ColumnString
-	Body      postgres.ColumnString
-	SenderIP  postgres.ColumnString
-	CreatedAt postgres.ColumnTimestampz
+	MessageID   postgres.ColumnString
+	GameID      postgres.ColumnString
+	SenderID    postgres.ColumnString
+	Kind        postgres.ColumnString
+	Body        postgres.ColumnString
+	SenderIP    postgres.ColumnString
+	CreatedAt   postgres.ColumnTimestampz
+	UnreadSeats postgres.ColumnInteger
 
 	AllColumns     postgres.ColumnList
 	MutableColumns postgres.ColumnList
@@ -65,29 +66,31 @@ func newChatMessagesTable(schemaName, tableName, alias string) *ChatMessagesTabl
 
 func newChatMessagesTableImpl(schemaName, tableName, alias string) chatMessagesTable {
 	var (
-		MessageIDColumn = postgres.StringColumn("message_id")
-		GameIDColumn    = postgres.StringColumn("game_id")
-		SenderIDColumn  = postgres.StringColumn("sender_id")
-		KindColumn      = postgres.StringColumn("kind")
-		BodyColumn      = postgres.StringColumn("body")
-		SenderIPColumn  = postgres.StringColumn("sender_ip")
-		CreatedAtColumn = postgres.TimestampzColumn("created_at")
-		allColumns      = postgres.ColumnList{MessageIDColumn, GameIDColumn, SenderIDColumn, KindColumn, BodyColumn, SenderIPColumn, CreatedAtColumn}
-		mutableColumns  = postgres.ColumnList{GameIDColumn, SenderIDColumn, KindColumn, BodyColumn, SenderIPColumn, CreatedAtColumn}
-		defaultColumns  = postgres.ColumnList{KindColumn, BodyColumn, CreatedAtColumn}
+		MessageIDColumn   = postgres.StringColumn("message_id")
+		GameIDColumn      = postgres.StringColumn("game_id")
+		SenderIDColumn    = postgres.StringColumn("sender_id")
+		KindColumn        = postgres.StringColumn("kind")
+		BodyColumn        = postgres.StringColumn("body")
+		SenderIPColumn    = postgres.StringColumn("sender_ip")
+		CreatedAtColumn   = postgres.TimestampzColumn("created_at")
+		UnreadSeatsColumn = postgres.IntegerColumn("unread_seats")
+		allColumns        = postgres.ColumnList{MessageIDColumn, GameIDColumn, SenderIDColumn, KindColumn, BodyColumn, SenderIPColumn, CreatedAtColumn, UnreadSeatsColumn}
+		mutableColumns    = postgres.ColumnList{GameIDColumn, SenderIDColumn, KindColumn, BodyColumn, SenderIPColumn, CreatedAtColumn, UnreadSeatsColumn}
+		defaultColumns    = postgres.ColumnList{KindColumn, BodyColumn, CreatedAtColumn, UnreadSeatsColumn}
 	)
 
 	return chatMessagesTable{
 		Table: postgres.NewTable(schemaName, tableName, alias, allColumns...),
 
 		//Columns
-		MessageID: MessageIDColumn,
-		GameID:    GameIDColumn,
-		SenderID:  SenderIDColumn,
-		Kind:      KindColumn,
-		Body:      BodyColumn,
-		SenderIP:  SenderIPColumn,
-		CreatedAt: CreatedAtColumn,
+		MessageID:   MessageIDColumn,
+		GameID:      GameIDColumn,
+		SenderID:    SenderIDColumn,
+		Kind:        KindColumn,
+		Body:        BodyColumn,
+		SenderIP:    SenderIPColumn,
+		CreatedAt:   CreatedAtColumn,
+		UnreadSeats: UnreadSeatsColumn,
 
 		AllColumns:     allColumns,
 		MutableColumns: mutableColumns,