The cables for HDMI 1.4 and 2.0 are supposed to be exactly the same, what changed between 1.4 and 2.0 was how the data is pushed through them (software) to support higher bandwidth. Thats the theory anyways, I think the older cables are a bit shittier sometimes so swapping newer cables in works for some people.
I still have this problem on my 7000 PS4 Pro occasionally, like maybe 3-4x a week and I've tried a TON of different cables. It happens a lot more when my PSVR (2.0) is hooked up inline, if I disconnect it from the chain it happens a lot less. I also have an xbox one X and it almost never happens with that, and I've swapped cables around so each system is using the same ones. I just wonder if its some weird signaling thing between PS4 and TVs.
Keep in mind when HDR is turned on the PS4 Pro (or X) can't do RGB 4k with HDR, they MUST switch to YUV 420. I suspect one of the issues is when HDR is on it switches to YUV 420 but then occasionally some handshaking must occur to try and renegotiate RGB mode which screws it up, which is why if you set it to YUV 420 all the time then it works since no resync is occuring. Not sure if its a TV HDMI sync problem or a console problem, my feeling its the PS4 since like I said I never see it on my Xbox (or Nvidia PC attached port).
I set my PS4 Pro to YUV 420 as well recently and zero reoccurences, since pretty much every game now I play has HDR enabled so its not a big deal being in YUV 420 all the time, for me at least.