I just did this recently… despite everyone’s insistence that it COULD work without an actual mobile phone number, I discovered that no, it can’t. In order to complete the setup, you MUST be able to enter a valid mobile phone number (not something like a Google Voice number.) After several months of trying, I gave up and got a real mobile phone.
I suspect the “doesn’t need a mobile number” information might predate the addition of SMS Protect because once SMS Protect was added to options and the four new backpack slots were added, the advertising for them said you had to add “an authenticator” not “authenticator & SMS” and I know for a fact that you did not get the four bag slots without adding SMS (because I had a keyfob authenticator for ages and didn’t get the four slots until I finally replaced it with a mobile phone and app.)
I realize the folks saying you CAN do it know more about this than I do, but my experience is that while you can run the app on a tablet, emulator, etc. you cannot complete the setup these days unless you have a valid mobile phone number to enter.
My thread from a few months ago: Mobile Autheticator options? - #10 by Keriss-kirin-tor