Actually, it is controlled at OS level rather than browser level. Android and iOS have both blocked autoplay background video until recent releases.
The attributes needed for autoplay to work are
The first two apply to Android and iOS, the third is iOS only.
Even then there are numerous exceptions that can prevent autoplay from working.
If the video has a soundtrack
if the device is in Low Power or Battery Saver mode
Thanks for posting about the issues you have encountered. I’d like to clarify that as it is stated in this Squarespace help article, video banners don’t always display on mobile. Their display depends on the visitor’s connection speed and browser version. That’s why it's recommended that a mobile fallback image is set.
If you’re experiencing an issue where neither mobile fallback image nor video background is loading on mobile, please reach out to Squarespace Customer Suppo