### 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)

Ref<Font> font = get_theme_font(SNAME("font"), SNAME("Label"));
	int font_size = get_theme_font_size(SNAME("font_size"), SNAME("Label"));
	return Vector2(0, font->get_height(font_size) * 3);
}
void EditorPropertyLayersGrid::set_read_only(bool p_read_only) {
	read_only = p_read_only;
}
Size2 EditorPropertyLayersGrid::get_minimum_size() const {
	Size2 min_size = get_grid_size();
	
	if (expanded) {
		const int bsize = (min_size.height * 80 / 100) / 2;
		for (int i = 0; i < expansion_rows; ++i) {
			min_size.y += 2 * (bsize + 1) + 3;
		}
	}
	return min_size;
}
String EditorPropertyLayersGrid::get_tooltip(const Point2 &p_pos) const {