For those unfamiliar, the informal distinction between type-1 and type-2 is that type-1 hypervisors are in direct control of the allocation of all resources of the physical computer, while type-2 hypervisors operate as some combination of being “part of” / “running on” a host operating system, which owns and allocates the resources. KVM (for example) gives privileged directions to the Linux kernel and its virtualization kernel module for how to manage VMs, and the kernel then schedules and allocates the appropriate system resources. Yes, the type-2 hypervisor needs kernel-mode primitives for managing VMs, and the kernel runs right on the hardware, but those primitives aren’t making management decisions for the division of hardware resources and time between VMs. The type-2 hypervisor is making those decisions, and the hypervisor is scheduled by the OS like any other user-mode process.
[1]: https://www.redhat.com/en/topics/virtualization/what-is-KVM
> The distinction between these two types is not always clear. For instance, KVM and bhyve are kernel modules[6] that effectively convert the host operating system to a type-1 hypervisor.[7] At the same time, since Linux distributions and FreeBSD are still general-purpose operating systems, with applications competing with each other for VM resources, KVM and bhyve can also be categorized as type-2 hypervisors.[8]