I have less issues with it after switching to Linux and using solar than I had on windows with the official app.
My PC is 6 years old and was high end back than, so its still mostly up to date, but a lot of the time the Logitech app simply refused to work. I had to manually downgrade it multiple times and it even caused two BSODs for me. My headset had issues with its connection and the soundfilter just sounded awful.
Since when are mouse inputs tied to individual frames?
Neither to action you perform nor the reaction from the Programm should be delayed, only the visual feedback you get.
Sure some older Programms don't use internal ticks bit instead use the framerate for that, which leads to a lot of issues with higher framerates as well, but they are few and far between.