The problem is pretty simple to pinpoint but sometimes impossible to fix, and it's 100% driver related.
Drivers by default have terrible settings, but they at least work for 99% of the people. Both NVIDIA and AMD refuse to fix the issues for the 1% that realize that their display quality is not as it should be.
Instead of just giving you immediate control over how the HDMI connections are handled, these companies insist on trying to baby their users and hide settings far and away, where they really don't need to.
It's clearly not an issue with your TV, as you had it working correctly with your last graphics card, however, convincing your NVIDIA card to display crisp output on a TV can be an exercise in frustration. It's difficult enough at times on an AMD card. I stopped using NVIDIA years ago for this reason.
The most obnoxious fix I've had to come up with is to override the EDID information that Windows retrieved from the screen and replace it with information that told the graphics card it was not a TV but a monitor instead, at which point, the output was magically fixed. This sort of idiocy could be fixed in the driver control panels with a single toggle switch, but it's not going to happen.
As far as supporting 4:4:4 color, that's not relevant, as the previous graphics card output clearly. Besides, at least on AMD, you can pick different pixel formats, so whether the TV supports 4:4:4 color or not, the card could be outputting something else. I have no idea if NVIDIA lets you choose different pixel formats or not, but I would be surprised if it wasn't possible, if not through their control panel software, through a Registry edit somewhere.