Telegram works great as a “replacement app” for people like me who don’t want to open their internal network via vpn or portforwarding or whatever. But: from everything I found, the current telegram bot integration does not support extracting location data for “send my location” messages. If it did, I could write an automation which updates the location info of my phone device tracker for times when the phone is not connected to our wifi, and allow for all the nice things that come with that (map view, automations, notifications to my partner, …)
Location messages do get received, but the one thing that’s missing is the actual location data. While googling the whole thing I stumbled over Telegram Bot: Location Messages · Issue #78676 · home-assistant/core · GitHub which describes the situation quite straightforward.
Telegram messages do support it overall (Telegram Bot API), just not as part of the HA integration (yet). Current status quo is in lines 114-117 in https://github.com/home-assistant/core/blob/dd39ddca2f3dd3f9d28e160a9b4904bcd58331c7/homeassistant/components/telegram_bot/init.py I think
I also found workarounds, like e.g. using Tasker to send a telegram command which adds long and lat as arguments in a regular command (Update a device_tracker GPS from a telegram command - #6 by hardkothari), but that wouldnt be needed anymore if the telegram bot could extract the needed fields directly.
So yeah, that’s it 
Thanks for listening