Gonna shamelessly bump this thread as a new PS4 Slim owner who is having this issue. Interestingly enough, when borrowing a friend's PS4 Slim the year before, it happened with theirs as well. However, I'm pretty sure it's not something that has happened to them when playing on their own TV + PS4 Slim setup. So it's seeming like there's some mass combination of TV, PS4 (Settings), and HDMI cables that can cause this problem.
I've since tried; the HDMI cable that literally came packaged with the PS4 (still happened), and 2 other HDMI cords in which it still happened with 1, and the other had the screen tripping out for a little bit (slight reddish fade to the screen, and audio almost cutting out). I've disabled HDCP, Deep Color Output, changed RGB Range to limited, and switched the resolution to a fixed 1080p instead of automatic, but I'm still getting some sort of video/audio issues some 30+ minutes or so into each session I play the PS4.
What bewilders me so much is that this is not an issue whatsoever with my Switch. I literally took the same HDMI cord that was connected to my Switch and used it for my PS4 when I first got it, and this 'handshaking' started happening. I'm assuming there's some specific set of settings I need to be switching my PS4 to that matches up with my TV's natural resolution to actually stop the issue for good??
I haven't finished reading through this whole thread, so I might find something that actually helps me stop this annoying shit from happening, but I thought I'd log this in as yet another individual with the problem, lol.