Icecast is good for audio brodcasting and well documented , can be use with vlc, or mixx for example

You don't really need a tool by itself, a few shell scripts should be enough.

I would use one shell script to loop through my song library and pipe data to some fifo.

Then you can read this fifo with ffmpeg and broadcast it somewhere.

The advantage of this approach is its flexible, easy to modify and you can use the tools you already have.

See https://trac.ffmpeg.org/wiki/StreamingGuide

Depending on what you need there is actually a long running open-source professional radio station (as in real FM radio, but also internet streaming) software called Airtime.

The original company developing it dropped support a while ago, but a fork called Libretime lives on.

Probably overkill for running an internet stream though.