I'm also having issues with nested virtualization. I am using Proxmox 5.3-5, and I'm currently getting the following error when trying to run Proxmox under a hypervisor:
TASK ERROR: KVM virtualisation configured, but not available. Either disable in VM configuration or enable in BIOS.
Any ideas? I like to run Proxmox in a test environment before making changes. I can do it on bare metal I suppose, but it's just a hassle. My CPU is an Intel Core i5 4570, which should be OK in theory.