### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

for (int i = 0; i < flag_rects.size(); i++) {
		if (i < tooltips.size() && flag_rects[i].has_point(p_pos)) {
			return tooltips[i];
		}
	}
	return String();
}
void EditorPropertyLayersGrid::_update_hovered(const Vector2 &p_position) {
	bool expand_was_hovered = expand_hovered;
	expand_hovered = expand_rect.has_point(p_position);
	if (expand_hovered != expand_was_hovered) {
		queue_redraw();
	}
	if (!expand_hovered) {
		for (int i = 0; i < flag_rects.size(); i++) {
			if (flag_rects[i].has_point(p_position)) {
				
				hovered_index = i;
				queue_redraw();
				return;
			}
		}
	}
	
	if (hovered_index != -1) {
		hovered_index = -1;
		queue_redraw();
	}
}
void EditorPropertyLayersGrid::_on_hover_exit() {