Is this actually GPL?

I see no LICENSE file in the repository (other than inside submodules) nor a reference to GPL or General Public License in any of the non-submodule files.

The only thing declaring a license is telegram.org. However, that is external to the repository and not very reassuring, as telegram.org may change at any moment or go down. And if Telegram bankrupts and telegram.org cease to exist, what license will this repo be under?

Also, if anyone copies this source code, they automatically violate the GPL even if this was actually covered by it, as they would be required to include a copy of GPL with it, missing from the original.

I wouldn't risk using this source code under the GPL until a proper license is included.

Quoting the GPLv2 itself (Terms and Conditions, #0; emphasis mine):

This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License.

And FSF:

Why does the GPL require including a copy of the GPL with every copy of the program? (#WhyMustIInclude)

Including a copy of the license with the work is vital so that everyone who gets a copy of the program can know what their rights are.

It might be tempting to include a URL that refers to the license, instead of the license itself. But you cannot be sure that the URL will still be valid, five years or ten years from now. Twenty years from now, URLs as we know them today may no longer exist.

The only way to make sure that people who have copies of the program will continue to be able to see the license, despite all the changes that will happen in the network, is to include a copy of the license in the program.

Start by checking the repository root for a LICENSE file and reviewing the non-submodule files for license notices, then compare them with the licensing statement at telegram.org/apps. Done requires resolving whether the repository has a clear, durable license statement and documenting or adding the requested license information.