Unless you have migrated your Lightroom Classic CC catalog, the only images that would count against your 20 GB cloud limit would be those that you have imported directly using Lightroom CC. Images synchronized from Lightroom Classic CC are smart previews and don't count against that 20 GB. Can't explain about the synchronization problem. Maybe someone else can help you with that.
I continue to try and make sense of using LR Classic and LR CC together.
You will have hard time making sense as they're not intended to be used together on same computer.
Yeah, I tried that for a while. Maybe that's why I'm so confused about it now. It just doesn't work very well (translated as at all, really).