The Jump button is realy only useful for manual smart, which is slightly faster than auto smart. i find myself spamming jump when i get to a vault/mantle location, and sliding manually instead of waiting for the auto to kick in.
i found if you let go of the smart you will continue to run but you wont do any parkour.
the SMART Button (LB/L2) doubls as the Sprint Button. If you press it, or let go and keep moving, then you Sprint. If you hold it or combo it with Jump or Crouch, then you do SMART moves.