There's no way to disable them in their mobile apps unfortunately without jumping through a couple hoops with something like a PiHole or using an alternative app on Android.
The alternative apps are great though. No ads, no tracking, included sponsorblock etc. I use libretube. Grayjay is also nice but a bit too commercial for me.
I don't use YouTube very often as I don't like the video format but sometimes I can't avoid it. And this makes it a lot more palatable.
Agreed, it is a very nice little interaction! It seems like they're animating the bubbles around a circle while randomly fluctuating the speed and radius at which they rotate. Clicking on a bubble centers it by setting the rotation radius to `0` and expanding the size.
Would be interested to know how they expand the bubbles as your cursor moves closer.