The sad part is that platform economies are mostly owned by US companies, and their internal (inside the platform) markets operate on a global scale. So far we haven't seen much external regulation here.

Clearly not enough, but there are laws (NetzDG) for censoring illegal posts in Germany.

Much more interesting and important, of course, will be regulation on actual platform mechanisms like vendor lock-in, Apple's non-compete app store policies and such.

Very true, although not with tech.