Way back when I switched from sata hdd’s to sata ssd’s, the experience in general was a lot snappier - but this was like ages ago and on Windows (8.1 or 10, can’t remember). Games loaded faster depending on the game.

Some months ago I was playing cyberpunk 2077 on win10 & sata3 ssd, and later on moved over to linux on pcie4 nvme on the same machine, and the loading times seem to be pretty much the same. But, admittedly way too much changed and fairly large timespan in between to draw any conclusive results.