To any1 interested, we can actually pass -stylesheet "style.css" path to it and override style! More here > https://forum.qt.io/topic/123100/change-link-colors-in-qt-assistant-with-a-dark-stylesheet

Finally, I have fresh installed it with Offline Installer, and it's working as expected. It seems isolated, so maybe nothing.

Thank you for having tried ;)

This can be marked as solved.

@SGaist

Thanks for the hint

@GrahamL

Well your screenshot
does look like it sort of fallback on simpler rendering engine so it would make sense.
Also it works, but looks different.