How to record soundcard audio and output to speakers with the BlackHole driver?
The steps below are for BackgroundMusic, another open-source driver which works pretty much the same as Blackhole. The same steps have also been verified to work with BlackHole.

In the Audio MIDI Setup.app create a Multi-Output Device and select the checkboxes for Built-in Output and Background Music.
Option+Click on the top-right speaker icon in the Mac menu bar and under Input Device select Background Music.
Under Output Device select Multi-Output Device as shown below.



You'll notice that after setting Output Device: Multi-Output Device the volume slider and the volume control keys won't work anymore. BackgroundMusic adds a menu icon in the top bar which you can click and use the volume slider in the dropdown that appears.


Both BlackHole and BackgroundMusic seem to cause occasional crashes of the Audio MIDI Setup app, and are not yet 100% stable and reliable (at least not on the MacOS version I tried), but they do work. I would classify both drivers as 'not-100%-stable' at the time of writing.