feat(#42): FIX projects can't add scenes (studio + admin)

Template copy now carries choose_mode from the content project → studio store gets
chooseMode; AddSceneMenu returns null for FIX/MusicVisualizer. Admin ProjectScenes
hides '+ صحنهٔ جدید' (shows an 'scenes defined in AE' note) for fixed modes. Verified
choose_mode=FIX flows end-to-end. (Visible admin nav link added earlier.)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/lib/studio-store.ts

@@ -159,6 +159,8 @@ export interface StudioState {
   audioVolume: number;
   sceneBackgroundColor: string;
   sceneAccentColor: string;
+  /** Project render mode (FIX / FLEXIBLE / MusicVisualizer / …). Empty until hydrated. */
+  chooseMode: string;
   past: StudioHistorySnapshot[];
   future: StudioHistorySnapshot[];
   layerClipboard: Layer | null;
@@ -249,6 +251,7 @@ export const useStudioStore = create<StudioStore>((set, get) => {
   audioVolume: 100,
   sceneBackgroundColor: DEFAULT_SCENE_BACKGROUND_COLOR,
   sceneAccentColor: DEFAULT_SCENE_ACCENT_COLOR,
+  chooseMode: "",
   past: [],
   future: [],
   layerClipboard: null,
@@ -757,6 +760,7 @@ export const useStudioStore = create<StudioStore>((set, get) => {
         parsed.sceneBackgroundColor ?? DEFAULT_SCENE_BACKGROUND_COLOR,
       sceneAccentColor:
         parsed.sceneAccentColor ?? DEFAULT_SCENE_ACCENT_COLOR,
+      chooseMode: parsed.chooseMode ?? "",
       past: [],
       future: [],
     });