Follow-up to my previous post : I've had Apple support on the phone multiple times, so far they haven't been able to provide a working solution.
Following their guidelines, I've done a factory reset of my iPhone 7 and have activated it *without* sync to my iCloud backup, meaning the device was totally blank. Even then, the issue persisted with black screens when playing videos in Safari (but I could hear the video sound). So in my opinion, we're most likely facing a software bug introduced with iOS 15.4 on (some? many?) iPhones 7.
I've had Apple Support on the phone again this morning, and they've had me record a video cap of the issue for their engineers to look into it. I encourage you guys to do the same, so they can gather as much data as possible and provide us a fix asap. In order to do that, you can get in touch with them here : Get Support