I interpreted that step as "once you click 'Auto Input Levels', drag the center triangle of the 3 at the bottom of the histogram to where you think the median of the histogram is". That middle slider defaults to being the midpoint of the other 2 sliders. I'm not sure if there is a smarter way to move it to the median beyond "looks about right".

I got this as a result https://i.imgur.com/RsXx3y2.jpeg and it certainly doesn't preserve the color of the rest of the image (there are probably more algorithmic steps needed for that) but it does seem to make highlight the same faint patterns much more clearly.

The levels tool maps a subset of the channel range to the full range, effectively changing the brightness and contrast in one step.

The center point controls the gamma correction, so you can map a biased distribution (mostly bright or dark for example) to be more evenly distributed.

That was the purpose of that step - move the midpoint slider to about where the peak in the histogram is, to get an evenly distributed range.

The low/high slider can be moved towards that to increase the contrast.

"Contrast" here will only apply to the A/B channels, which is the color information, so it's increasing the color contrast and unbiasing it, while keeping the luminance information.

Photoshop also can do the same transform, and interactively in the LAB colorspace (no need to combine/uncombine the channels first).

I just checked it using one of the photos on that page. The final colours are not the same, but the contrast enhancing ability is comparable