revert(nav): restore original room creation/join behavior

Reverts navigation changes that broke lifted state popover behavior.

Original behavior (now restored):
- Create room: Keep popover open, switch to invite tab to share code
- Join room: Close popover, stay on current page

The navigation changes caused the popover to close immediately,
breaking the lifted state pattern that was intentionally designed
to keep the popover open for sharing room codes after creation.

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

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

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

@@ -78,10 +78,8 @@ export function AddPlayerButton({
             name: data.name,
             gameName: data.gameName,
           })
-          // Close popover
-          setShowPopover(false)
-          // Navigate to the room page (singular - fetches current room)
-          router.push('/arcade/room')
+          // Popover stays open, switch to invite tab to share room code
+          setActiveTab('invite')
         },
         onError: (error) => {
           console.error('Failed to create room:', error)
@@ -112,8 +110,6 @@ export function AddPlayerButton({
             }
             // Close popover
             setShowPopover(false)
-            // Navigate to the room page (singular - fetches current room)
-            router.push('/arcade/room')
           },
         }
       )