In addition to tapping and selecting a different action group using the group button to the left of the keyboard, you can also swipe up and down to quickly change.
TIP: Swipe up and down on extended keyboard to swap groups
brentacPrime
#2
Adding to this, I made an action group with nothing but links to 5 frequently visited drafts. Tapping the keys on the extended keyboard dramatically speeds up going to those drafts.