The main target of the Godot Engine are game developers. But Godot's easy workflow and functional UI elements, makes it also a good fit for non-game applications. There are already some out there you may know, like Pixelorama, an Open Source 2D sprite editor.
I think that'll depend on the application. For a painting program like Pixelorama, the logic being attached to the UI element, like the brush button dealing with the brush specific logic, it makes sense, it should be intuitive to look for how it works on a "brush.gd" file.
With Godot, the logic tends to reside within scenes and, without taking a look at Pixelorama, I would wager that most of the logic is already centralized, as I suspect the scene containing all the canvas-interacting buttons (fill, color pick, brush, select, etc) are all coupled in the same scene. Most of the time, you'll have 1 script per scene, so all the logic of that scene is "centralized"
From my very hazy recollection, that decentralization was a problem with Delphi/Lazarus (Pascal), each UI component had a separate file to handle its logic. Might be remembering it wrong.