I have a 2018 CX-9 so my set-up might be different but worth a try for you to see if this works.
In my car the shortcut buttons around the rotating wheel in the centre console direct to the last used application. For example, if i am listening to apple music and go to google map, then pressing the music button will bring me back to apple music. But if i am listening to the FM radio and go to goole map, then pressing the music button will bring me back directly to the fm radio (out of apple carplay). Pressing the nav button beings me back directly to google map in apple carplay.
It is a shortcut that allows you to go back to each service without having to use the long way of getting in and out of apple carplay (or android auto).
This should work the same way for sirius xm.
If it opens pandora and you want to listen to sirius, do like a previous poster said. Hold the home button to get out of android auto and back to mazda system. Go to the sirius music and select it to play music. Holding the home button will go back to android auto, or you can press nav to go directly to google map.