In the documentation, the "Hard Light" blending mode is described as follows:

Similar to Overlay. A combination of the Multiply and Screen blending modes, switching between both at a middle-lightness.
Hard Light checks if the color on the upper layer has a lightness above 0.5. Unlike Overlay, if the pixel is lighter than 0.5, it is blended like in Multiply mode, if not the pixel is blended like in Screen mode.
Effectively, this decreases contrast.
(see https://docs.krita.org/en/reference_manual/blending_modes/lighten.html#hard-light)

This description does not describe Hard Light. Indeed, Hard Light works exactly like Overlay with upper and lower layers exchanged. Where the action of Overlay depends on the value of the upper layer, the action of Hard Light depends on
the value of lower layer. Check the source code where Overlay is defined as:

inline T cfOverlay(T src, T dst) { return cfHardLight(dst, src); }

Note that a few other blending modes are described by referring to Hard Light or Overlay and might also be incorrect.