chicagoskycam
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The age of the display shouldn't matter. It's purely a matter of 'does this display have HDR or not?'. A TV without HDR made last week and a TV made without HDR 10 years ago should register the same. If it has HDR, use it, if not, use SDR. But the PS5 method is inaccurate.
How bad it looks may depend on your display. The better/more accurate your black levels, the more obvious the problem will be.
I guess but it may be an issue with your display overall as people with other non-HDR displays don't have this issue. I have not gamed on a Plasma in over 10 years so the issue doesn't surprise me.