Weird chirping sound coming from new PC (video/sound)

I don't hear anything, but that may be down to my poor monitor speakers.

Chirping/screeching is an odd description to hear though. Initial thoughts (without being able to hear it) would be either an HDD or an AIO pump?

You're recording from outside the case (at least, that's what it looks like to me).
Popping the side panel off may help you identify the general direction of the noise.
 


Maybe I described it wrong. It's like a faint beep, but on a such a frequency that I'm actively losing my mind.