It’s interesting that you brought this up. I feel like it is not super unusual. I experience something similar, and many people that I have spoken to have described their own version of it.
I call my version “brain radio”.
When my mind is idle, I hear music. Sometimes it is literally like listening to the radio (minus the disc jockey’s voice and commercials). I will hear a song in its entirety, a brief pause, and then a completely different song. This can go on all day, fading away when I am focused on a task, and returning when I’m not. Other times it will be a snippet of a song, or a single song on repeat for a period of time.
When it happens, I hear lyrics, instruments, etc - just as though the sound was coming from an external source.
In all cases, the songs seem to be ones that are familiar to me, though they are often ones that I could not possibly have heard (on the radio, or a movie soundtrack, for example) in decades.
At this exact moment, the song is “Love is Alive” by Gary Wright, from his 1975 album “The Dream Weaver”.
I have had this for as much of my adult life as I can remember. My wife, who is not hearing impaired, has a similar experience. Sometimes I will hear her call out from another room, and it will be something like “Dust in the Wind!!”, and I will reply with “Dream Police!” For both of us, it is predominately songs that are from our preferred era and genres - mostly pop music from the 1960s through the early 2000s.
Very occasionally, it will be a song that I know, but was never “popular music”. In one case recently it was a kind of nonsense song that my grandmother used to sing when I was very little, called “Mairzy Doats” (apparently published in 1943, more than 20 years before I was born). There’s no way I have heard that externally for at least 50 years.
It doesn’t really bother me, I just see it as one of the oddities that makes me, me.