feat(gateway): persist chat sessions and messages in PostgreSQL

- store: new chat_sessions/chat_messages tables with CRUD, ILIKE message
  search, and auto-titling from the first user message
- context: optional Persister on the sliding-window store — messages are
  saved asynchronously on Add, sessions not in memory are restored from
  the database on Get
- orchestrator: ProcessInput/FinishRound now carry userID so persisted
  messages have an owner
- api: real session handlers (list/create/delete), message history and
  clear endpoints, working message search and three-format export
  (markdown/txt/json), fixing the short-ID panic in export
- main: migration, store wiring, ctxStore persister adapter

Tests: chat store handler lifecycle (fake store), context persister
save/restore, stub auth login flow updated.

backend/services/gateway/api/router_test.go

@@ -25,7 +25,7 @@ func TestHealth(t *testing.T) {
 
 func TestLoginAndProtectedEndpoint(t *testing.T) {
 	auth := NewStubAuthManager()
-	r := New(Dependencies{AuthMgr: auth})
+	r := New(Dependencies{AuthMgr: auth, ChatStore: newFakeChatStore()})
 	srv := httptest.NewServer(r)
 	defer srv.Close()