I have an AVR and the quirky HDCP issue I've always had with my Pro and never any other console, is once per session it'll have a BLACK SCREEN flash for a few seconds, OR a multicolored one flash. Sometimes unplugging the HDMI cable and plugging it back in "cures" it but it's very annoying, searching online, it appears many people have this issue, but Sony just ignores it, as it's possibly a hardware issue.
It's odd but it might be the HDMI cable, have you tried using the current Xbox cable on your PS4 Pro? Sometimes HDMI cables can be odd, but if the cable doesn't resolve the issue, then it's Sony's issue. Another thought is, do you need 4k? I don't so I turned on force HDCP 1.4 or something in the safe mode menu.