I stream iTunes (Mojave) to an Apple TV gen 3, which has toslink, into a DAC.  
I made  a folder in iTunes and added radio stations ( Internet Radio, listed in library from iTunes ).
This feature is not available in the new Apple Music (Catalina) which replaced iTunes.
Can you download the last version of iTunes into Catalina and proceed as before?
To stream a radio station from its website requires using Airplay which is not desirable. Plus, can't easily 
choose from, say, 10 different stations. 
09f118d5 0302 48c2 94f4 773faa506010jackiejr

I haven't yet upgraded to Catalina but I've found this solution to your question. Hope it helps. Thanks for asking it because it will help me once I upgrade.

Good luck,
I'll give it a try and report back. Thanks Tom!!!
I just can't get the suggestion from Apple to work. 
Hello @jackiejr 

I still haven't upgraded to Catalina yet. However, I noticed the instructions on the Apple Support web link for Catalina Music app that I sent you back in April aren't any different than what I'm doing in iTunes in Mojave.

I followed the instructions in the settings for "Connect to an Internet Broadcast" section.

I pasted this link (BBC World Services) in the box for Open Stream:

Then I hit OK. It created a box in my music window - looks like an album. Once I clicked on it and clicked on the PLAY arrow, it took several seconds before it started to stream. It didn't start right away AND you should watch the Music apps transport control to see it change from Play to Pause ( = ) meaning it is streaming. I was surprised it took longer than I expected.

Hope this helps,

If you're streaming from iTunes on your Mac to the Apple TV, it is already using AirPlay. Since there's no hardwire digital audio connection between the Mac and Apple TV.

(For what it's worth, I cannot get radio stations to show up when I search either.)
I'm still stuck. Here's an example of what I'm trying to accomplish.  


There is a choice of a few genres. Classique Plus for example.

How do I get this into the song folder in Music?

You see, France musique is not a choice when you search in Music.

Also, to nekoaudio, Airplay is not activated when I'm streaming radio stations to appletv. I'm talking Mojave here.  thanks