Nicely done!

Possible improvement to consider would be cursor key navigation, to allow rapidly moving to the correct emoji (whereas, currently, it seems either the mouse is needed or tabbing forward/backward is needed, which can be time consuming).

Edit → I don't currently use Telegram, and I guess you may not see this adjustment to the review, but to clarify the above a little: I like to use the keyboard more and the mouse less. It would be great if I could open the emoji picker, type in whatever I'm looking for and then use the up/down/left/right keys to navigate to the one I want; hit enter and continue.