feat: Add Picture-in-Picture floating video + fix local track visibility

- New PictureInPicture component: draggable floating window that shows
  active stream when navigating away from voice channel, with LIVE badge,
  snap-to-edge, click-to-navigate-back
- Fix VoiceUser to check actual track presence instead of boolean flags
  for video rendering
- Add LocalTrackPublished/LocalTrackUnpublished events to useLiveKit
  so local screen share and camera show immediately in VoiceGrid
- Add pipCollapsed state to uiStore

packages/web/src/stores/uiStore.js

@@ -31,7 +31,9 @@ export const useUIStore = create((set) => ({
     }),
     voiceChatOpen: false,
     voiceFullscreen: false,
+    pipCollapsed: false,
     toggleVoiceChat: () => set((state) => ({ voiceChatOpen: !state.voiceChatOpen })),
     toggleVoiceFullscreen: () => set((state) => ({ voiceFullscreen: !state.voiceFullscreen })),
     setVoiceFullscreen: (fullscreen) => set({ voiceFullscreen: fullscreen }),
+    setPipCollapsed: (collapsed) => set({ pipCollapsed: collapsed }),
 }));

packages/web/src/stores/uiStore.ts

@@ -36,9 +36,11 @@ interface UIState {
   closeUserProfile: () => void;
   voiceChatOpen: boolean;
   voiceFullscreen: boolean;
+  pipCollapsed: boolean;
   toggleVoiceChat: () => void;
   toggleVoiceFullscreen: () => void;
   setVoiceFullscreen: (fullscreen: boolean) => void;
+  setPipCollapsed: (collapsed: boolean) => void;
 }
 
 export const useUIStore = create<UIState>((set) => ({
@@ -80,7 +82,9 @@ export const useUIStore = create<UIState>((set) => ({
 
   voiceChatOpen: false,
   voiceFullscreen: false,
+  pipCollapsed: false,
   toggleVoiceChat: () => set((state) => ({ voiceChatOpen: !state.voiceChatOpen })),
   toggleVoiceFullscreen: () => set((state) => ({ voiceFullscreen: !state.voiceFullscreen })),
   setVoiceFullscreen: (fullscreen) => set({ voiceFullscreen: fullscreen }),
+  setPipCollapsed: (collapsed) => set({ pipCollapsed: collapsed }),
 }));