feat: sync URL with selected game mode

Add Next.js router integration to update URL when user selects
a game mode in GameControls. Now when selecting:
- Practice Mode → URL becomes /games/complement-race/practice
- Steam Sprint → URL becomes /games/complement-race/sprint
- Survival Mode → URL becomes /games/complement-race/survival

This makes URLs shareable at any point in the setup flow.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

apps/web/src/app/games/complement-race/components/GameControls.tsx

@@ -1,10 +1,12 @@
 'use client'
 
+import { useRouter } from 'next/navigation'
 import { useComplementRace } from '../context/ComplementRaceContext'
 import type { GameMode, GameStyle, TimeoutSetting } from '../lib/gameTypes'
 
 export function GameControls() {
   const { state, dispatch } = useComplementRace()
+  const router = useRouter()
 
   const handleModeSelect = (mode: GameMode) => {
     dispatch({ type: 'SET_MODE', mode })
@@ -12,6 +14,8 @@ export function GameControls() {
 
   const handleStyleSelect = (style: GameStyle) => {
     dispatch({ type: 'SET_STYLE', style })
+    // Update URL to match selected game style
+    router.push(`/games/complement-race/${style}`)
   }
 
   const handleTimeoutSelect = (timeout: TimeoutSetting) => {