We're going off-topic here regarding mouse latency, but not sure about that. My mouse works excellently for 4k and no difference from 1080p, but I'm using an RTX 2070 super so probably helps with rendering at 4k. There's some other bottleneck on your system which was causing that.Tested these 5 years back - there is sufficient lag in the mouse - more evident when gaming.
I guess that will pull up other questions on mouse polling (Logitech G9 ) - that is set at 1000 ,DPI changes on the fly as needed.
( besides using G602 )
If this was a significant problem for 4k, it would be widely known and no gamer would buy 4k monitors. Anyway, I guess let's just leave it at that. I personally find 4k significantly sharper than 1080p and don't see any downside at least on my system.