Does Radiccio have a menu bar icon for controlling playback?

Radiccio does not provide its own menu bar icon. However, macOS has something like this built-in. Try clicking the Control Center icon, which looks like this:

When music is playing in Radiccio, you should see playback controls, as well as some details about the currently playing song.

If you would like a dedicated menu bar icon for this, go to System Settings > Control Center > Control Center Modules > Now Playing, and select the option “Always Show In Menu Bar”. That icon looks like this:

Note that both of these menus work for various other apps on your Mac that play audio or video, not just Radiccio. So, you may see other apps in there also, if they have played something recently.