I have a bluetooth aluminum Apple keyboard. I think it's the same one you get with iMac systems, though don't quote me, as I didn't get mine with a mac; I bought it sand-alone.
Using iOS 16.2 with my iPhone 13 Pro Max, I know hitting Command+H takes you to the home screen. That said, I could have absolutely sworn that hitting Command+H twice quickly in succession was how you access the app switcher, but undoubtedly I'm wrong. All that is appearing to do is keep accessing the home button over and over.
What have I clearly missed? I used to know with a bluetooth keyboard how to do this, but it's slipping my mind.