Phoenix is the mobile wallet, but there's also a "headless" API version of the software that can run on a desktop or server. But to use phoenixd you need other software like Alby (nprofile…fy4z) Hub (https://guides.getalby.com/user-guide/alby-account-and-browser-extension/alby-hub/introduction) if you want a UI on top of it.
One issue you'll have with the phoenix mobile app and bolt12 is your phone app needs to be running to receive payments, at least I just tried to send a little payment to you above bolt12 "offer" and it didn't work because I suspect your phoenix app isn't running. But if you use phoenixd on an always on machine this wouldn't be a problem.
And, yes you can tell you have a bolt12 "offer" because it starts with `lno`.