### 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)

if (!is_inside_tree()) {
		return;
	}
	updating_theme = true;
	if (sub_inspector != nullptr) {
		int count_subinspectors = 0;
		Node *n = get_parent();
		while (n) {
			EditorInspector *ei = Object::cast_to<EditorInspector>(n);
			if (ei && ei->is_sub_inspector()) {
				count_subinspectors++;
			}
			n = n->get_parent();
		}
		count_subinspectors = MIN(15, count_subinspectors);
		add_theme_color_override("property_color", get_theme_color(SNAME("sub_inspector_property_color"), SNAME("Editor")));
		add_theme_style_override("bg_selected", get_theme_stylebox("sub_inspector_property_bg" + itos(count_subinspectors), SNAME("Editor")));
		add_theme_style_override("bg", get_theme_stylebox("sub_inspector_property_bg" + itos(count_subinspectors), SNAME("Editor")));
		add_theme_constant_override("v_separation", 0);
	} else {
		add_theme_color_override("property_color", get_theme_color(SNAME("property_color"), SNAME("EditorProperty")));
		add_theme_style_override("bg_selected", get_theme_stylebox(SNAME("bg_selected"), SNAME("EditorProperty")));
		add_theme_style_override("bg", get_theme_stylebox(SNAME("bg"), SNAME("EditorProperty")));
		add_theme_constant_override("v_separation", get_theme_constant(SNAME("v_separation"), SNAME("EditorProperty")));
	}
	updating_theme = false;
	queue_redraw();
}
void EditorPropertyResource::_update_preferred_shader() {