There's no specific "single tap" functionality; however, there is "Touch Binding" which may be akin to what you're looking for.

Touch Binding as Mouse Click by itself is no good for navigation on Windows because it acts like it's always holding the "click", so it'll constantly draw the selection rectangle. It'll act like you're holding the click when you're trying to navigate with the touchpad.

Actually pressing the touchpad to click is terrible with the DualShock 4, because it tends to move erratically as you press the touchpad before actually registering the click, which makes it very imprecise. The best use for "pressing" the touchpad is as an additional menu button.

In any case, I've found an improvised way of implementing this "laptop trackpad"-style Tap to Click behavior. Works really well.

1. Under "Desktop Configuration", customize the touchpad. Make sure its "Style of Input" is set to "MOUSE"
2. Select "Additional Settings"
3. Select "Touch Binding"
4. Now you need to have two Activators: one for "Regular Press" and another for "Long Press". The Regular Press will be the "tap to click". The "Long Press" will just detect if you kept on touching the trackpad, which means you didn't just tap, you're actually holding the touch, so it should stop interrupt the click action so it doesn't "hold" the click. To do this:
5. Bind "Regular Press" to "Left Mouse Click" and set "Interruptable" to "On" (important because the "Long Press" activator will interrupt this one).
6. Create a new activator and bind it to "Long press". Bind it to EMPTY (the minus sign on the top right of the virtual keyboard). This will make it so that it will do nothing, but it's gonna be enough to interrupt the first activator and stop the "clicking all the time" behavior". Set "Toggle" to "Off" and
7. Set "Long Press Time" to a very low value (just move the gauge all the way to the left, then 2 times to the right).

And you're done. If you're using a DualShock 4, you can mirror these settings for each side of the touchpad so you get "Tap Left Side to Right Click" and "Tap Right Side to Left Click" or reverse if you're left handed, or just use unified touchpad.

All in all, I'd say Steam Configuration is great and robust enough to allow for these kinds of solutions, but some common behaviors like this should be easier to implement. InputMapper and DS4Windows both have a single checkbox to make DS4 touchpad work like this.

Also, some Steam Controllers users have expressed their desire to make the Steam Controller Touchpad work like this (being able to tap to register a click instead of actually clicking the touchpad), so it's kinda weird that there's an easy "Double Tap" setting, but we have to create a workaround to make "Single Tap" to work.

Thank you for this. I had much success with your guide.

I have one improvement maybe for desktop use. I added a third activator for double press (left mouse) with the delay 0.180 to be able to double tap and hold to select, like on a touchpad. The only thing that is a little bit messed up and awkward is double click to select one word. The timings are a bit strange. I've ended up leaving the second long press activator on 0.091 (as close to half I could get it). Not sure what is optimal here, but the end result is that I have to double tap kind of slowly to be able to select one word. I do this more rarely than double tapping and holding though, so it's definitely okay.

Thanks the #2 still works with the second gen steam controller! I created a shared layout with this configuration for anyone interested. "Desktop with tap to click"