Dana Biosphere is the quieter hiking, if you want days that aren't Petra crowds. You walk from highland village toward the rift, sometimes all the way to Feynan. Ibex country, long descents, and a biosphere that runs on rules. This region is essentially Tafilah. Give it its own nights. A photo stop from a Petra taxi isn't the hike.
Canyon descents to Feynan
The classic is a guided hike down through the reserve. It's knees, heat and water discipline, not a boardwalk. Shorter rim walks exist. The full Feynan descent is an improver day. Stay in Dana village or Feynan, depending on which way you're walking.
Fit it after Petra, not instead of sleep
Do Petra, then Dana, then Rum or Aqaba. Don't sandwich a full biosphere day between two 4am starts. Open the Book here tab for reserve timings and whether porters or transfers are included.