Screen recording is handled in an interesting way. If you start the recording while in the Telegram app, it just freezes after the 3-second countdown and never starts. It times out after about 10 seconds. If you switch to another app before that, it starts the recording, but if you try to switch back to Telegram the recording freezes halfway through the app switcher animation. Protected media is also blanked out in the app switcher.

It's different from apps using DRM like Netflix, where it usually just shows a notification saying "failed to start screen recording".

I just tested it again, and as the user below notes, it has some way of interfering with screen recording. However this is not 100% reliable. as I was able to create a screen recording of the media in the group's media overview page and zoom in as usual.

The trick was to start the screen recording out of Telegram, open it (if you're on the actual page it will freeze the recording interestingly) but once you get to the media overview page, the screen recording works again and you can capture whatever you want. I have been able to record everything without problem once incl the chat, but this is probably only effective in some cases.

As it turns out, regular screenshots also work on that page. My testing was not super thorough I suppose, for something I quickly did while trying to fall asleep...

I'd guess it just uses the same iOS framework parts that are used already for Netflix and other streaming services to blank out the content. In that case screen recording would also be taken care of.