ui/phase-14: auto-sync order draft + always GET on boot + header headline

Replaces the manual Submit button with an auto-sync pipeline driven
by `OrderDraftStore`: every successful add / remove / move
coalesces a `submitOrder` call so the engine always mirrors the
local draft. Removing the last command sends an empty cmd[] PUT —
the engine, repo, and rest model now accept that as a valid
"player cleared their draft" state.

`hydrateFromServer` is now invoked unconditionally on game boot so
a fresh device picks up the player's stored order, and the local
cache is overwritten by the server's view (server is the source of
truth).

Header replaces the static "race ?" + turn counter with a single
headline string `<race> @ <game>, turn <n>`, sourced from the
engine's Report.race + the lobby's GameSummary.gameName + the live
turn number, with a `?` fallback while any piece is loading.

Tests:
- engine: empty PUT round-trips, repo round-trips empty Commands
- order-draft: auto-sync sends full draft on every mutation,
  rejected response surfaces error sync status, rapid mutations
  coalesce, server hydration overwrites cache
- order-tab: per-row status flips through the auto-sync lifecycle,
  remove → empty cmd[] PUT, rejected → retry button
- inspector overlay: applied + valid + submitting all participate
  in the optimistic projection
- header: live race / game / turn rendering with fall-back

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

game/internal/router/order_test.go

@@ -60,16 +60,25 @@ func TestOrderRaceQuit(t *testing.T) {
 
 	assert.Equal(t, http.StatusBadRequest, w.Code, w.Body)
 
-	// error: no commands
+	// empty cmd[] is a valid PUT — the player cleared their draft;
+	// the engine stores the empty batch and answers with the
+	// canonical `UserGamesOrder` envelope. ValidateOrder receives a
+	// zero-length variadic and the response carries no commands.
 	payload = &rest.Command{
 		Actor: commandDefaultActor,
 	}
+	exec := &dummyExecutor{}
+	emptyRouter := setupRouterExecutor(exec)
 
 	w = httptest.NewRecorder()
 	req, _ = http.NewRequest(apiCommandMethod, apiOrderPath, asBody(payload))
-	r.ServeHTTP(w, req)
+	emptyRouter.ServeHTTP(w, req)
 
-	assert.Equal(t, http.StatusBadRequest, w.Code, w.Body)
+	assert.Equal(t, commandNoErrorsStatus, w.Code, w.Body)
+	assert.Equal(t, 0, exec.CommandsExecuted)
+	var stored order.UserGamesOrder
+	require.NoError(t, json.Unmarshal(w.Body.Bytes(), &stored))
+	assert.Empty(t, stored.Commands)
 }
 
 func TestOrderRaceVote(t *testing.T) {