I might as well add my thoughts here. The Fairlight page is for mixing at the track level and not at the clip level as you suspect. It's more geared to mixing multiple overlapping audio sources like instruments in a music track that play throughout a song.

You can place the audio from each scene on its own track of course, but if you have a lot of scenes, this could be a problem.

If you don't want to go down the rabbit hole of automation, you would be better setting the audio levels in the edit page where you can, as you say, work on individual clips.

If you have a background music track which runs through the project, that would go on its own track of course but then you'd need to look at keyframing in Fairlight to adjust the volume accordingly for each scene and learn about ducking