I imagine what those custom brightness apps do is not magically increase the brightness, but change the various pixels' brightness in accordance to some method/algorithm such that you see what appears to be brighter whites when placed next to certain other colors.

It's not what is implied by the parent post - where the mac is limiting the brightness only to have the app unlock it.

No, I believe the issue is Apple limits the top half or so of the brightness/backlight level for HDR content only. The apps allow it to be used for normal non-HDR content.

I think it's just a matter of some "I need HDR" syscall.