How do I add a receptacle from a switch located on the end run of an existing split receptacle?
That switch box contains 2 hots and no neutral. So without running any new wire, your only option would be to re-wire the outlet so that it is no longer switched and use the switch box as a junction box.

Here's a before and after diagram. Note that the "neutral" between the switch and the outlet is actually your white wire that has been relabeled hot.



Thinking about it again, you could make your NEW outlet switched in this configuration.