It's VMs. The overhead is not nearly as bad as you think it is, especially with the highly tuned cloud hypervisors. I've seen dual EPYC monsters running 300+ VMs. Server CPUs are basically designed for that kind of workload these days.

Virtualization tech is really, really good. On my desktop, I have a VM that runs Windows+SteamOS with a passed through GPU, game on it and everything. You wouldn't know it's a VM. The overhead is so low that I just let it run in the background most of the time. When it's idling it basically just occupies RAM. You can't really feel the VM on the host either, everything is as responsive as usual. As long as there's enough resources for everyone, you can barely tell it's a VM or not.

Modern CPUs have extensions to handle it at the processor level, and most operating systems have good paravirtualized devices, so there's not a whole lot of overhead left other than the guest kernel and processes.