I actually looked into Telegram but decided HTML5 push notifications are “better” for what I needed because I don’t have to sign up for another platform (less things I have to install on my wife’s phone the better). Your example can easily be done with HTML5 if you use chrome/firefox and I do something similar but for turning off lights that were possibly left on.
So for push notifications, you can do most the same stuff, but with telegram you can embed images and stuff, where as with notifications you’d probably link them (html5 only supports icons for example).
One other advantage that Telegram has is it is really a chat client, not a push notification. Therefore, you can send a command from any telegram client to your HA server without being prompted first (via a notification). That allows you to do stuff like this - HASS TeleBot (Telegram Bot) Of course, there are plenty of other ways to interact with HA (REST API for example), so if that is a benefit to you is for you to decide.
Really it comes down to how you want to use it. I decided that going with HTML5 made more sense (no extra app, I can push notifications to my work PC)
As for easier to set up, well, that depends on if you think verifying domains and setting up SSL certificates is hard.