Yurts are genuinely rare — a few dozen across the whole country — so a park that has one usually has exactly one. They are booked solid in season and almost never appear in a normal search, because there are too few of them to show up.
We track live availability at 34 campgrounds with yurts across 4 states, on Recreation.gov and 13 state park systems. Every one is rechecked every 15 seconds, around the clock, so when a booked site frees up you hear about it in seconds rather than finding out weeks later that it was open for an hour.