I recall years ago reading about FCC licenses for low-powered FM stations (range significantly less than the 60 miles of most current stations). I won’t say “amateur” but the implication was they were non-commercial, almost hobby. Not sure if that’s still a category.
Plus, there are plenty of software programs I recall reading about starting when MP3’s were first a thing, where you could program a playlist and the station (or internet streaming) would play that unattended. There is of course a licensing process for broadcasting music too (or streaming) based, I think, on audience numbers. If you just want it around your property, there are low power FM transmitters - I wonder what drive-ins used to push sound out? There were gizmos to put your headphone output to the FM in your car, before cars had audio-in plugs.
I guess the other question is where you would get equipment if you started a radio station. I don’t imagine commercial FM band broadcast equipment is an off-the-shelf item; and range is line of sight, so you would want a tall tower or a good hill. When I’ve driving away from the big city, I get to the point where the FM signal fades off when I’m over a hill and comes back as I climb the next one.
One review says this gets about a mile and a half range…