The campsite/campground limit is not enforced by the Recreation.Gov site (otherwise it would be a lot harder for scalpers to game the system), but is enforced (when enforced) at the campgrounds during your stay.
During your stay, the campground staff (sometimes the hosts, sometimes it's park rangers) go around each campsite to see that everyone has the proper campsite permit. They'll also take note of the vehicles (including their license plates) parked at each individual campsite. If they noticed that a vehicle has been at the campground longer than seven nights, they can evict the people at the campsite for overstaying at the campground. That's how it usually works.
Frankly, I don't know how strict they are about the enforcement. Personally, I don't try to abuse the system since there's only a very limited amount of campsites in Yosemite Valley and it would be unfair to others to try to stay longer than the seven nights limit they have in place for camping inside Yosemite Valley. One can legally camp in a campground for up to 14 nights in Yosemite,
but outside of Yosemite Valley and Wawona (between May 1st and Sept. 15th).
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