chore(extension): bind relay lifetime to browser context (#804)

src/browserServerBackend.ts

@@ -30,7 +30,6 @@ import type { Tool } from './tools/tool.js';
 export class BrowserServerBackend implements ServerBackend {
   name = 'Playwright';
   version = packageJSON.version;
-  onclose?: () => void;
 
   private _tools: Tool[];
   private _context: Context | undefined;
@@ -75,7 +74,6 @@ export class BrowserServerBackend implements ServerBackend {
   }
 
   serverClosed() {
-    this.onclose?.();
     void this._context!.dispose().catch(logUnhandledError);
   }
 }