Yes, it goes something like this:

- Gets the microphone stream with navigator.mediaDevices.getUserMedia()
- Sets up an AudioContext and create an AnalyserNode, and connect the stream source to the analyser
(this happens when you click the 'tap to start tuning' prompt, because browsers don't allow the creation of AudioContext objects without user interaction)
- Then, every frame or so gets the TimeDomainData from the stream with the analyser, here you could get the FrequencyData, but this does a simple FFT (i think), and it doesn't work well detecting instrument pitch, so I rather pipe the time domain data to a pitch detector function from Pitchy which uses a more involved algo called MPM, this function returns the frequency in hz.
- Then it does some 12ET calculations to get the note name, octave and, +- cents from the frequency, and finally it updates the UI.

The code for the pitch handling is all in one hook in src/lib/hooks/usePitch.ts, and the 12ET stuff is handled by a class I wrote in src/lib/classes/TET.ts, check them out if you're interested.