feat(history,gateway): D4 会话未读/已读游标 — unreadCount + POST /sessions/{id}/read + session_read 广播

- chat_sessions 增 read_at（毫秒，与 chat_messages.created_at 同单位）；迁移 0010 并把既有会话回填为各自最新消息时间（升级当天不误报）
- ListSessions 单查询派生 unreadCount（无 N+1，复用 idx_chat_msgs_session_created 覆盖索引）
- MarkSessionRead 只前进 MAX(read_at, ?)；未知会话 ErrSessionNotFound；游标方法挂在网关消费侧窄接口（沿用 GetMessage/messageLookup 先例，避免污染 runtime 接口与其 fake）
- POST /api/v1/sessions/{id}/read：writeAuth + 400/404/501，成功广播 session_read、失败路径不广播
- Docs/api-client v0.37（§1 unreadCount / 新行 8a / §3.9 session_read / §4.2 用法）
- 含迁移回填测试、store/handler 测试与变异验证；顺带把 migrate_pinned_test 的「回退一步=0009」硬编码改为对迁移数量免疫

internal/services/gateway/history.go

@@ -26,6 +26,12 @@ type historySessionSummary struct {
 	// per-session request. It is omitted for a session with no messages. Content is
 	// already truncated by the store.
 	LastMessage *historyLastMessage `json:"lastMessage,omitempty"`
+	// UnreadCount is the number of messages newer than the session's read cursor
+	// (D4), derived in the same list query. It is always returned (0 when nothing
+	// is unread) so a client can render/clear the badge without a second call. The
+	// cursor is session-scoped and single-owner: reading on any one end clears the
+	// badge for every end of the account.
+	UnreadCount int `json:"unreadCount"`
 }
 
 // historyLastMessage is the wire shape of the last-message preview in a session summary.
@@ -79,6 +85,7 @@ func (s *Server) handleHistorySessions(w http.ResponseWriter, r *http.Request) {
 			CreatedAt:   m.CreatedAt,
 			Pinned:      m.Pinned,
 			LastMessage: toHistoryLastMessage(m.LastMessage),
+			UnreadCount: m.UnreadCount,
 		})
 	}
 	writeJSON(w, http.StatusOK, out)