Yeah, it's an important topic! I also enjoy the GMTK videos, really in-depth and actually helpful for devs!
Thanks for the suggestions. Using 2 variables for the different input modules is a good idea!
The problem regarding the frame rate dependency comes from Unity's Cinemachine Input Provider (I guess) or maybe the Axis Control itself. I found a similar bug inside the Cinemachine bug tracker, maybe that's my problem. Input/Timings are handled by Cinemachine, I haven't changed anything here :(