so all third-party syncing apps will have to deal with this somehow?

My understanding is that the process killing applies to everything that is not directly tied to the Apple ecosystem, so probably. So far I haven’t found a way around it.

There probably isn’t a way to selfhost an iCloud server somehow, is there?

That would be nice, but this IS Apple we are talking about here. As far as I know that isn’t even an option for the US Government.