On macOS with Qt 5.13.x QtWebEngine does not display system colors when launched with the --single-process command line option.
It worked with Qt 5.12.x

I think, that the changes in qtwebengine/src/3rdparty/chromium/content/browser/theme_helper_mac.mm are responsible for the behaviour.

I attached a simple example, which calls the system colors demo site from above. The results are in singleprocess.png and multiprocess.png

Chromium Commit:
https://chromium.googlesource.com/chromium/src/+/0694f7c1f92d46137fe536f1fde23963fccac0b5