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/order.go

@@ -1,7 +1,6 @@
 package handler
 
 import (
-	"errors"
 	"net/http"
 
 	"galaxy/model/order"
@@ -18,6 +17,10 @@ func PutOrderHandler(c *gin.Context, executor CommandExecutor) {
 		return
 	}
 
+	// An empty `cmd` array is a valid PUT: the client clears its
+	// local order draft and expects the server to mirror that
+	// state. The engine stores the empty batch so the next GET
+	// returns the same empty list with the new `updatedAt`.
 	commands := make([]order.DecodableCommand, len(cmd.Commands))
 	for i := range cmd.Commands {
 		command, err := repo.ParseOrder(cmd.Commands[i], validateCommand)
@@ -26,10 +29,6 @@ func PutOrderHandler(c *gin.Context, executor CommandExecutor) {
 		}
 		commands[i] = command
 	}
-	if len(commands) == 0 {
-		errorResponse(c, errors.New("no commands given"))
-		return
-	}
 
 	result, err := executor.ValidateOrder(cmd.Actor, commands...)
 	if errorResponse(c, err) {