The TT system is first come first served but still books campsites like a regular RV park. Their system is setup to have each site get a reservation.
When this happens- there is availability at one or more spots for each individual site but there isn’t a reservation open for any single site for the duration of stay that you want.
The answer is to reach out to customer service (my preference is via chat). They can piece together a reservation for you on multiple campsites for the stay request. You’ll see it in your “My Trips” as multiple reservations.