fix(nav): navigate to room after creation from (+) menu

When creating a room from the /arcade page using the (+) button:
- Add room to recent rooms list
- Close the popover
- Navigate to the room page immediately

This fixes the UX issue where users would create a room but
remain on the /arcade page without any clear indication of
how to access their new room.

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

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

apps/web/src/components/nav/AddPlayerButton.tsx

@@ -72,8 +72,16 @@ export function AddPlayerButton({
       },
       {
         onSuccess: (data) => {
-          // Popover stays open, switch to invite tab to share room code
-          setActiveTab('invite')
+          // Add to recent rooms
+          addToRecentRooms({
+            code: data.code,
+            name: data.name,
+            gameName: data.gameName,
+          })
+          // Close popover
+          setShowPopover(false)
+          // Navigate to the room page
+          router.push(`/arcade/rooms/${data.id}`)
         },
         onError: (error) => {
           console.error('Failed to create room:', error)