I managed to make a template for Telegram alerts and firing the test alert works fine. If I intentionally shutdown Node exporter on one of our servers to test if an actual alert will be sent, nothing happens. It’ll only get sent if I update the contact point, for example disabling resolved messages.
I am using Grafana 8.5.2 with the unified alerting system. E-Mails work just fine.
welcome to the 
forum, @greeenflaash
have you checked out these open issues regarding the Telegram notifier?