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>

ui/frontend/tests/e2e/game-shell.spec.ts

@@ -35,8 +35,9 @@ test("shell mounts with header / sidebar / active-view chrome", async ({
 }) => {
 	await bootShell(page);
 	await expect(page.getByTestId("game-shell-header")).toBeVisible();
-	await expect(page.getByTestId("race-name")).toContainText("race ?");
-	await expect(page.getByTestId("turn-counter")).toContainText("turn");
+	await expect(page.getByTestId("game-shell-headline")).toContainText(
+		"turn",
+	);
 	await expect(page.getByTestId("view-menu-trigger")).toBeVisible();
 	await expect(page.getByTestId("account-menu-trigger")).toBeVisible();
 });