Perhaps some of this applies to GTK, instead of Geany.

I am satisfied with the locations of the toolbar, sidebar, message window, and the notebook tabs as I've configured them.

However occasionally I will temporarily like to move things around. Currently there is limited flexibility to do so, and one has to access preferences to do this.

I suggest the following features:
(1) Ability to move widgets around (like the side-bar) with snapping. Things can always be locked in place to avoid annoyances due to accidental moving.
(2) Autohide. I find this annoying myself generally. But I would find it helpful in some circumstances. Again, autohide works best with an "pin-in-place" button.
(3) Fading: I don't think I've seen this anywhere before, and hence might be difficult to implement, but I think I'll find this very helpful. I suggest that some/all widgets outside the editor be dimmed (low contrast/brightness) at all times, but that they get lit up again when they receive focus, or a mouse hover. I keep the sidebar visible always, and I think fading it will reduce clutter. I need to look at the info on the sidebar only when I'm intending to jump to another file/symbol. Likewise for the notebook tabs, which I look at only when I'm switching tabs using keyboard/mouse.