Part of https://linear.app/comm/issue/ENG-2688/backup-service-reuse-single-blob-client-instance

Now these functions do not need to be async anymore. The connection errors are now handled inside the spawned Tokio task. I improved logging the connection error (it is now displayed immediately instead of finishing and waiting for the terminate() method to handle errors). Also, the start() signature can be simplified not to return Result

Depends on D6386

Ran backup service integration tests. Killed blob service. Ran tests again and checked if the erorr is handled as expected