turn library music volume down in final cut

That is a valid point.

I can easily see how monitoring that clip in your screenshot is a problem. Do most of them look (and sound) like this one?

Unfortunately, I don't see a way to make those changes in the browser - unless you actually import from the music browser to your library. Probably not what you wanted, but may serve as a workaround: drag a bunch of candidate music to an event in your library, adjust, choose, and delete those that you don't want.

If a clip is already in your FCP library, you can make adjustments in the Inspector, and you can do it for many clips at once - just select them all and lower the volume.

It is up to you how you edit your timeline, including the audio level.

You could lower the volume of any clips you want, or apply a limiter or compressor effect. There are endless possibilities. I expect that others much more versed in audio work can give more specific advice.

Also, you can enlarge the waveforms in the timeline appearance,

and turn on the audio meters (Command-Shift-8) to better monitor your audio.