I have had this problem too with a Logitech G915 keyboard and G502X plus mouse, both connected wirelessly through the Lightspeed adapter and directly connected via USB cable. I think the issue lies with Logitech and Windows 11 (maybe a bad feature update) as this problem has appeared in other games as well for me. I just noticed it in FFXIV 1st as I'm a lot more active on the controls compared to some of the other games I was playing. The problem also doesn't always occur right away and may take a couple hours or more that the PC is powered on before showing.