>
it has to switch out the whole stack (4k or 8k) even when there are only a few bytes that belong to that particular task (because it has no way of knowing which bytes those are)This reads to me like you believe the OS must memcpy/move the whole stack out of the way on a context switch. It doesn't; the other thread has other, dedicated memory its stack, and on a context switch, the stack pointer is simply adjusted to point at the other stack.
Assuming Java's fibers work similar to other green thread implementations, green threads/fibers work similarly — it's just a pointer change, except the adjustment is done in userspace.
(And, to some degree, the OS does know what bytes are stack for any given task. It's whole pages, yes, but that allows the program to manage it otherwise. But I think most green-thread/userspace threads are similar: the stack is preallocated ahead of time and left to the thread to manage. Sure, you might not know the exact range, but you don't really need to? Go, I think, is an interesting outlier here; IIRC, it dynamically expands and contracts the allocated space on the stack in response to the application's demands, though I do think they had some interesting issues w/ loops thrashing allocations if they fell along an allocation boundary. I think they've also long since fixed that issue.)