So the LG C4 is going to be the best latency you are going to get, period. I WFH and sit all day on screens with static elements and so have resisted moving to an LG or other OLED monitors for my main desk; I bought an ASUS 48 OLED but ended up putting it on my daughter's desk. When we were sitting up the Switch2's though I realized I have the 3rd and 4th best monitors in the house, and man that sucks, as my son's desk has a TCL 43 with awesome HDR10 while my Sony 43X720Es were great when I bought them in 2017 or whenever, 4k60 isn't the state of the art anymore and they don't even really do HDR at all. I have been waiting on a 42/43 Mini-LED TV to hit the market but in that time frame, the TV size I want has jumped the shark; TVs are bigger now 55+ and really 70-75 or larger and monitors have stopped at 32". That LG OLED is cream of the crop and while Samsung makes some good TVs in that space QN90D/F is right there, I just hate to spend that money ($1200+)when what I have works well enough. Sony had a good LED monitor of some tech that hit many of the sweet spots (120Hz, VRR, multiple HDMI 2.1 inputs, in that right size, etc) K85 but the last year they made them was 2022 and there isn't any stock anywhere to be found, even on Ebay.
About your current dilemma: My manager has a LG 42 C2 and loves it; uses it for work and for gaming, swears he has no burn in after 2 years. I don't know how many hours outside of work he put in on it or how many static elements, etc. I know he does the health stuff regularly, clean up etc. I was just so scarred by plasma burn in and even early LCD burn in that I still can't pull the trigger on anything where that is a chance of happening. I have two Sony's, so I could (and would only ever) retire one but I may just spend the extra $400 on the Mini LED if end up having to buy a monitor sooner rather than later. I guess if I start to burn one in I could always put it on a work bench or move it somewhere else. Quite the dilemma of my own.
If latency if your true measure; it won't get any better than the LG C4/C5.