Hey there, glad your metronome is working well.
The "beep" output is just a simple signal designed to trigger external equipment like a motor, light array, etc. It's not really meant to be used with headphones or as an audio signal; It's definitely a logic signal instead of an audio signal.
The PWM pin is the audible-frequency PWM signal that is used to drive the piezo speaker to make the audible beeps. The Tactile Metronome uses two different pins to interact with the piezo. Pin 5 is the PWM output that drives the beeps on the piezo. Pin 13 is the analog input pin that is used to sense the taps on the piezo. If you want to use an external piezo for either input or output, it's suggested that you cut a trace on the circuit board that will disconnect pins 5 and 13 from each other. If you look at the image below, the red lines are traces on the top of the PCB and the green lines are traces on the back side of the pcb. If you look between pins 5 and 12 you can see a green line that has an odd-looking horizontal section. If you take off the battery holder you can use a sharp knife or razor blade to carefully cut through that horizontal part of the trace. Once it's cut, the on-board piezo is only useful as input (you can also solder an external input piezo between ground and the little hole labeled "p" just below/left of the on-board piezo). You can then connect an external output piezo to the hole labeled "P" at the bottom of the board.
If you want to reprogram the microcontroller to adjust the sensitivity, that'd be really easy to do. There's one value called PIEZO_THRESHOLD that sets how big of a voltage spike is required to recognize an input tap. Currently it's set to 60, which means 60/
Hope that makes sense! Let us know if you have other questions.