Thank you very much for the stack-trace and debug logs. I have come to
understand that the crash doesn't relate to libappindicator. Telegram
crashes when it's initializing GTK on
Telegram/SourceFiles/platform/linux/linux_libs.cpp:109. I saw it was
already fixed in new version [1].
Could you run their binary of v1.0.14 version [2] to confirm my guess?
(You were already trying with v1.0.27, weren't you.) Also it'd be great
if you try to remove libappindicator1 package, and then run
telegram-desktop, or if you install libappindicator3-1 package and run
Telegram. (I'm only interesting whether the program crashes again or
not, I daresay yes, and this behavior doesn't depend on libappindicator.)
Besides you can try a workaround with GDK_BACKEND environment variable.
Try to set it to "x11".
[1]: https://github.com/telegramdesktop/tdesktop/commit/8884cb1
[2]: https://updates.tdesktop.com/tlinux/tsetup.1.0.14.tar.xz