So today I randomly started getting the "Network Error" when exporting one of my projects while using 5.7.0 and the crack. I tried upgrading to 5.8.0, and while the crack continued to work fine for other projects, I still couldn't export this one particular project even though it's worked fine before. However, I did find a semi-workaround:
Eliminating the "Speed Curve" effect on one of my clips got my project to export. I was able to leave all other effects as is, including PRO ones.
I'm not sure if that's a bug with Capcut, my particular installation, or a sudden complication with the crack, but if you are having trouble exporting try eliminating Speed Curve and/or hunt for other similar effects that might be causing the error.
I'm curious if anyone else can duplicate this.