+1 that this is ridiculous..
I'm running an aerial photography studio and having blurry noisy videos for my clients first impression is absolutely not acceptable.
One workaround that i settled on is simply uploading the videos to Youtube as unlisted, then linking them in the Squarespace background.
This has one problem though, everytime your video loops, it flashes black for half a sec.
Uploaded videos dont do that. But again, 1080p is unacceptable for professional sites.
Frankly unbelievable that Squarespace hasnt resolved this, not even on a Business plan.
I'm gonna try uploading / linking Vimeo instead to see if that solves the flashing black on loop.