With my new Mac (on macOS 10.15.7 Catalina) I haven't installed any desktop audio recording software. Previously I've used Audacity, Wiretap Studio (from now defunct Ambrosia Software), Capto, and GarageBand. I'd rather not download a separate application if I can use GarageBand instead. But although GarageBand works fine with regular sound inputs it doesn't record desktop audio.

Enter Soundflower, an open source MIDI extension. Not the most intuitive to setup. Once installed open Audio MIDI Setup and you should see Soundflower (2ch) and Soundflower (64ch) devices. Create a new device (e.g. Beats + Soundflower) then add one of the Soundflower devices and your normal output device (I use my Beats Wireless). Now you have an audio output device where you can listen to the audio as you record.

In GarageBand (v10.3.5) create a new project which adds a new track:

Track Type = Audio --> Microphone
Input = Input 1
I want to hear my instrument as I play and record = off
My instrument is connect with: Soundflower (2ch)
I hear sound from: Beats + Soundflower

Now with this project you can play desktop audio and record it. Then you can use Share --> Song to Music... to export to Music app.