I have some clues on what's wrong with the webengine on 6.4.3, more later
I tried running qtwebengineprocess from a command line with --help and got an error about no OpenGL implementation being available. That reminded me of some hack I made in some of the OpenGL code. I've now reverted those hacks and will attempt to fix another way.
Depending how sore my foot is this afternoon, I hope to have more updates in a few hours.