Closer is eMacs ^s and ^r. You csn type ^stext and it will jump to the next instance of ‘text’. Keep hitting ^s and you continue searching.

Pedantically it’s a keystroke less than / <enter>.

The distinction is that the Leap key is more like a shift key bs how vim and emacs works.

Yup. Jef was big on eliminating modes, so came up with the LEAP "semi-mode". Emacs ctrl-s enters a mode that you use ctrl-g to escape (or at least that's what I use, there are probably many other ways to exit search mode.)

Subsequent ctrl-s presses in emacs is the equivalent of the "USE FRONT" / "LEAP AGAIN" key press.

You're absolutely right! I was weighing up whether to analogise it to Emacs or vi, and in my haste I made the wrong choice.