Thanks for playing!
You haven’t missed many instructions by skipping the texts. They are mostly flavourtext. The instructions are given above the ghost that appears when you pick up an upgrade. Also in this game, like in most auto runner games, there is no turning around.
You are right in the assumption that the passage you are dying at requires a walljump, which will be unlocked later on.
The climbing upgrade unlocks the path at the second scroll where you pick up the manual respawn upgrade and cannot get out of the pit by jumping only. You are not the only one to have this issue, maybe I should have telegraphed more that there is a way there by putting up a sign next to the wall you have to climb or something.