feat: Automatically recover from frozen live streams (#2569)

- Closes: #2099

src/camera-manager/camera.ts

@@ -60,6 +60,7 @@ export class Camera {
   protected _eventCallback?: CameraEventCallback;
   protected _destroyCallbacks: DestroyCallback[] = [];
   protected _entity: Entity | null = null;
+  protected _initialized = false;
 
   constructor(
     config: CameraConfig,
@@ -79,6 +80,10 @@ export class Camera {
     return this._entity;
   }
 
+  public isInitialized(): boolean {
+    return this._initialized;
+  }
+
   async initialize(options: CameraInitializationOptions): Promise<Camera> {
     // Freeze a single HASS snapshot for the whole (async, multi-step)
     // initialization so every step observes a consistent entity world; live
@@ -116,6 +121,7 @@ export class Camera {
       }
     }
 
+    this._initialized = true;
     return this;
   }