iPhone "disabled" when trying to enter recovery mode
Looks like the way to resolve this is:


Tap volume up
Tap volume down
Hold side button
When the "slide to power off" screen appears, let go of the side button.
Slide to power off the phone completely.
Once the phone is shut off, make sure it's plugged into iTunes.
Hold the side button to power on and continue holding it until the recovery screen shows up.


Therefore, the key is to shut it down completely instead of using the restart method as Apple recommends.