Atleast for gmail , google has their own telegram bot (has the blue tick beside it) , just type “gmail bot” in your telegram search bar , it will have a bot with a blue tick beside it
I also use this, but it's not gotten any updates since it was introduced. I would like to rewrite a bot from scratch, but the Gmail bot's initial offering is still good enough that I don't have the motivation.
The worst problem it has is the lack of multi-account support. The reply functionality is also a bit buggy. I generally only use it as a read-only client.