To locate the noise I would suggest the tried and true way I've done it for decades. Put the car up on ramps, and have someone else bounce the car and put you hand on the rubber bushings, you should easily be able to feel which one/s are squeaking.
Just a guess, it's the sway bar to frame bushings, you should be able to work some spray silicone in and around the bar without disassembling it. Worst case scenario you might need to loosen the mounts and get some silicone around the sway bar.
In my experience, it's likely a rubber bushings from that noise in the video, rubber will squeak, urethane is even more prone to squeaking, hence the reason most urethane bushings come with silicone grease to be applied during installation.
I hope this helps.............
