I wanted to dive deeper into the point that Xen is not part of Linux. Although it is true that the Hypervisor is not part of the Linux Kernel, all the enablers that enable guests (DomU) and Xen hosts (Dom0) are in the Kernel. The Hypervisor itself doesn't need to be part of the kernel. As long as Xen is delivered via a a distro's package manager, I don't need to care whether Linux is the Hypervisor, or whether it is not. At the end of the day, Xen and KVM make different design decisions, leading to different trade-offs and thus one or the other setup will be better for different workloads.
The Xen Hypervisor delegates a lot of functionality to the Dom0 kernel (typically Linux, but can also be NetBSD). And although there are Xen specific drivers for the PV interface in the kernel, these are essentially just shims that call the device drivers in the Dom0 kernel and are part of the PV interface.