Also, why put a backdoor in the client if the server sees pretty much every message in plaintext?
You can install the Telegram FOSS client, at least in an Android cellphone.
For me, Telegram FOSS client stopped working.
Telegram server side is open source?
The Telegram server code is not open source. It's been in the "we will open source everything at some point in time" limbo for years.
Durov has said server code will not be open sourced since it would help countries block them more easily. They use many methods to avoid being blocked by government.