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/handler/command.go

@@ -2,7 +2,6 @@ package handler
 
 import (
 	"encoding/json"
-	"errors"
 	"fmt"
 	"net/http"
 
@@ -33,7 +32,12 @@ func CommandHandler(c *gin.Context, executor CommandExecutor) {
 		commands[i] = command
 	}
 	if len(commands) == 0 {
-		errorResponse(c, errors.New("no commands given"))
+		// `PUT /api/v1/command` is the immediate-execution path —
+		// running an empty batch is a meaningless no-op, so we
+		// reject it with `400` rather than rely on the validator.
+		// `PUT /api/v1/order` keeps an empty list (the player
+		// cleared their draft) — see `OrderHandler`.
+		c.JSON(http.StatusBadRequest, gin.H{"error": "no commands given"})
 		return
 	}