Are the backpacking sites first come first serve? And if so how busy are they around the middle of May?

Highly recommend to reserve online. There are sites close to the rock and some quite a hike away. I doubt you can secure any same day campsite.

They're only available via online reservation. They're usually booked several weeks in advance

They have campsites and trails. You can rent a campsite but on the weekends you have to get there 1st.