### 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)

Node *parent = get_parent();
	EditorProperty *parent_property = nullptr;
	while (parent && !parent_property) {
		parent_property = Object::cast_to<EditorProperty>(parent);
		parent = parent->get_parent();
	}
	if (parent_property) {
		EditorShaderPicker *shader_picker = Object::cast_to<EditorShaderPicker>(resource_picker);
		Object *ed_object = parent_property->get_edited_object();
		const StringName &ed_property = parent_property->get_edited_property();
		
		if ((Object::cast_to<GPUParticles2D>(ed_object) || Object::cast_to<GPUParticles3D>(ed_object)) && ed_property == SNAME("process_material")) {
			shader_picker->set_preferred_mode(Shader::MODE_PARTICLES);
		} else if (Object::cast_to<FogVolume>(ed_object)) {
			shader_picker->set_preferred_mode(Shader::MODE_FOG);
		} else if (Object::cast_to<CanvasItem>(ed_object)) {
			shader_picker->set_preferred_mode(Shader::MODE_CANVAS_ITEM);
		} else if (Object::cast_to<Node3D>(ed_object) || Object::cast_to<Mesh>(ed_object)) {
			shader_picker->set_preferred_mode(Shader::MODE_SPATIAL);
		} else if (Object::cast_to<Sky>(ed_object)) {
			shader_picker->set_preferred_mode(Shader::MODE_SKY);
		}
	}
}
void EditorPropertyResource::_viewport_selected(const NodePath &p_path) {