### 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)

RID ci = easing_draw->get_canvas_item();
	Size2 s = easing_draw->get_size();
	const int point_count = 48;
	const float exp = get_edited_property_value();
	const Ref<Font> f = get_theme_font(SNAME("font"), SNAME("Label"));
	int font_size = get_theme_font_size(SNAME("font_size"), SNAME("Label"));
	const Color font_color = get_theme_color(is_read_only() ? SNAME("font_uneditable_color") : SNAME("font_color"), SNAME("LineEdit"));
	Color line_color;
	if (dragging) {
		line_color = get_theme_color(SNAME("accent_color"), SNAME("Editor"));
	} else {
		line_color = get_theme_color(is_read_only() ? SNAME("font_uneditable_color") : SNAME("font_color"), SNAME("LineEdit")) * Color(1, 1, 1, 0.9);
	}
	Vector<Point2> points;
	for (int i = 0; i <= point_count; i++) {