In this instance, I would say your attention has been adjusted, not your ear's ability to perceive sound. Our ears don't have a control setting or a means of adjusting incoming sound levels (though I'm certain when an ambulance with loud siren drives by, we all wish we did).
What you are experiencing is a prioritization of the sound by your brain in relationship to other sounds.
You put the sound on before you go to sleep. Your brain accepts that incoming sound as non-vital, non-threatening sound. (Radio, meant to soothe, supposed to be there, relegate this sound to innocuous)
Come dawn, new and novel sounds appear. For our brains, the new and novel could indicate a threat, so your brain prioritizes that sound over the known and considered innocuous sound (your radio) which it has heard all night. Birds, tennis balls on courts are distinctive enough your brain would prioritize them even though you know in your conscious mind neither is an actual threat.
As you waken, your brain then reminds you there is still another sound in your environment which is not threatening and yet still prevalent (your radio) prompting you to decide if you want to do anything with the non-threatening sound.
Yes, this is an oversimplification of a very complex process of sound prioritization but most modern science bears this out. As a curiosity, our minds are predisposed to seek out information which may be vital to us, hence the reason conversations held by other people who are on the phone are so distracting because our brains dislike hearing things which may be necessary to our survival but only hearing half of the conversation.
As I was reminded there are some involuntary control elements built into the ear via:
the tensor tympani muscle whose role is to dampen sounds (mainly internal ones such as chewing)
and the stapedius muscle which dampens the ability of the stapes vibration and protects the inner ear from high noise levels, primarily the volume of your own voice.
You can thank the stapedius muscle for making your voice sound so strange to you when you hear it on a recording. You have never truly heard your voice until you hear an external recording and playback of it!