Which Firefox functionality was used in the Telegram vulnerability? Isn’t this all about the desktop app?

None, I'm not sure what the other user was talking about

Telegram wanting to be single instance means that it has to use some serialization, and it not escaping semicolons enables a part of the attack.

What does "being single instance" mean here?

	▲	g-b-r 2 hours ago \| parent [-]
		That only one instance of Telegram can run at any time. And if you open a Telegram link it will open in the existing instance. Windows uri handlers actually always create a new process, though; so if you want this single instance behavior, you have to do some check at the start of the process and communicate the uri to the previously running process (as explained in the article).