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
Squarespace has identified some issues with the display of background videos on mobile that should now be fixed for 7.1 sites. For any issues you may experience with background videos on your site, please contact Squarespace Customer Support. For now, I am locking this post.