The current Spyder Checkr software does work with the new released the Adobe Photoshop Lightroom Classic version 13.
Adobe has changed the location of the HSL (Hue, Saturation, Luminance) slider in the Lightroom Classic 13 version. Therefore, you will not see the adjustments in the HSL slider from the Spyder Checkr presets as in previous Lightroom Classic versions in the "HSL / Color" section.
Here you will see, how to access and the HSL (Hue, Saturation, Luminance) slider in the Lightroom Classic 13:
Launch Lightroom Classic and go to the Develop area.
Now locate the section Color Mixer:
and maybe you will have to select in the Adjust drop down menu "HSL":
Now you will see the HSL slider as normal:
You will see the HSL slider adjustments generated by Spyder Checkr after applying a Spyder Checkr preset, and you can edit the HSL sliders as you wish.