Nothing shows up when something makes a sound
The app has to be running to hear anything — look for the waveform icon in your menu bar. It only lists sounds that happened after it started, so it cannot tell you about a ding from before you launched it.
The play button is greyed out
That means no recording was captured for that sound. Usually it is because macOS has not been given permission to record system audio: open System Settings › Privacy & Security › Audio Recording and make sure What Just Pinged Me? is allowed. Sounds too quiet to hear are also discarded rather than kept as silent clips.
Web audio says "Safari" instead of naming the page
Naming the tab requires permission to talk to your browser. Open System Settings › Privacy & Security › Automation and allow What Just Pinged Me? to control the browser you use. If you would rather not, everything else keeps working.
A sound is credited to the wrong thing
Some apps play audio through helper processes, and browsers do not tell other apps which tab is making noise — so the app uses the tab you are looking at, which is right nearly all the time but not always. If you find a case that is consistently wrong, please say so; those reports are what make it better.
Still stuck
Email [email protected] and include your macOS version and what you were doing when the sound played.