My touch bar almost always has "Display Connected: [Mirror Displays] [Extend Desktop]" on it. I can fiddle around and get it to show app-specific things, or hold Fn to see the F keys, but most of the time I'm using it it shows those useless multi-monitor buttons.

I'm sure there's some setting somewhere that defaults to showing whatever the layout for the in-focus app is, but it's failed to make me care enough about it to try to figure it out.