Telegram-FOSS (the FOSS friendly fork you can find on F-Droid, not the official app on Play Store) maintainer here. Telegram is NOT a "secure messaging app".
That comes from upstream's README.md. I've never payed any attention to it, but now that you've pointed it out, I'm seriously considering changing that paragraph, or adding a note/disclaimer somewhere.
After all these years and promises, server's code is still closed, federation is nowhere to be found, their update/commit policy for the official Android app is a joke [1] (they even closed its issue tracker), and I'm really tired of their "trust us, we're not evil" policy [2].
If you haven't switched to Matrix/Riot, do it right away.
As one of the resident cryptography nerds: Matrix/Riot seems to be in every way better than Telegram. I still need to review it before I can wholesale recommend it, but it was audited by NCC Group previously.
Matrix is a federated chat protocol. It is like IRC or XMPP but synchronizes history and uses HTTP-based protocol. There are bridges to IRC, XMPP, and Gitter.