[PM-17658] Fix persist route to clear if service worker dies (#13382)

* Add way to convert TaskSchedulerService to RX Scheduler

* Add docs to `toScheduler`

* Rollback combined subscription change.

* Move to barrel file

* Expand `toScheduler` documentation

* Add TaskName to Doc Example

* Ensure register is called on service worker start

apps/browser/src/background/main.background.ts

@@ -607,6 +607,7 @@ export default class MainBackground {
     this.popupViewCacheBackgroundService = new PopupViewCacheBackgroundService(
       messageListener,
       this.globalStateProvider,
+      this.taskSchedulerService,
     );
 
     const migrationRunner = new MigrationRunner(