I recently encountered a situation where Safari would not play background videos in web pages! I initially assumed the page was broken... until I realized mine was the only iPhone with this behaviour, yet I am on the latest iPhone and iOS version. I finally figured what was different with my setup, and how to solve this issue.
Every other web page on the Internet with a purported fix is totally wrong. It has nothing to do with Safari Experimental features, nothing to do with the Safari cache, nothing to do with Screen Time, nothing to do with your ad-block extension, nothing to do with the proxy or DNS settings, or any other rubbish.
The reason
Web pages with background videos do not auto-play because I had turned on the Accessibility feature called Reduce Motion!
Reduce Motion is a toggle in the Accessibility settings.
I dislike the zooming animation that accompanies app launches and home screen navigation. Safari honours this setting as a request not to auto-play background videos and in fact does not even load the first frame or poster frame of the video.
The downside is that this leaves certain web sites using background videos riddled with blank (black) spaces, and it is not obvious that something is missing. Background videos also do not have playback controls, leaving no way to manually start playback. No screenshot would do this justice, but you may visit the specific website where I discovered this: here.
The upside is no pesky auto-playing background adverts or videos!
The solution
One could turn off Reduce Motion entirely...
But for me, I have a Control Center toggle to Accessibility Shortcuts. The next time I encounter a situation where I do want background videos, I can quickly toggle the setting from Control Center.
Now you know.
Both screenshots of Apple documentation, retrieved this date the 10th of September 2023