However, YouTube timestamps do not work in Telegram Desktop. For example, the message https://t.me/anthro_fun/456 contains YouTube timestamps in Telegram for Android, but in Telegram Desktop they're rendered in plain text (not clickable).
The usual explanation for this behaviour is that Telegram for Android renders a video player (and thus can rewind and fast forward that player at will), but in Telegram Desktop a hyperlink that leads to YouTube is just that (a hyperlink) and all it does is visiting YouTube's website.
However, YouTube's website has a feature that looks like a solution to the problem: if a parameter “?t=1324” is added to YouTube's video URL (or “&t=1324” if that URL already has at least one other parameter), then YouTube will fast forward 1324 seconds before playing the video designated by that URL. (Providing minutes and seconds is also supported, try https://youtu.be/tH2w6Oxx0kQ?t=1m02s for example.)
Telegram Desktop should acknowledge that YouTube's feature and should start attaching such URLs to the timestamps. Each timestamp would be just a hyperlink that opens a web browser and points to YouTube's web site; nevertheless, it still would point to the designated second of the video.
Telegram Desktop could even go one step further than Telegram for Android: Telegram Desktop could support timestamps in messages that won't have video players for YouTube URLs in Telegram for Android (such as YouTube URLs in captions under images meant as cover artworks for YouTube videos, see https://t.me/holmogortalks/13768 for example).
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Implementation details: https://github.com/telegramdesktop/tdesktop/commit/f2e4a5a35a7522fe6d8345e8816c3d36336bb5a4