When a real thread is allocated from a virtual thread to another, the JVM needs to save into the heap the stack of the first virtual thread and restore from the heap the stack of the second virtual thread, see slide 13 of [1]. This is in fact called mounting/unmounting as already pointed out, and occurs via Java Continuation, but from the JVM perspective this is a context switch. It's called JVM and the V stands for Virtual, so yes, it's not the kernel doing it, but it's happening, and it's more frequent the more virtual threads you have in your application.

[1] https://www.eclipsecon.org/sites/default/files/slides/JavaLo...