repos: Make a best effort to update external service timestamps

Created by: ryanslade

There were certain error cases before where we would just return an error and not update the timestamp on the external service. These would lead to the last_synced_at timestamp growing older and older until it triggered an alert. It would also cause us not to backoff when syncing these problematic services.

Closes https://github.com/sourcegraph/sourcegraph/issues/35529

Test plan

Unit tests updated