### 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)

}
}
void EditorPropertyResource::update_property() {
	Ref<Resource> res = get_edited_property_value();
	if (use_sub_inspector) {
		if (res.is_valid() != resource_picker->is_toggle_mode()) {
			resource_picker->set_toggle_mode(res.is_valid());
		}
		if (res.is_valid() && get_edited_object()->editor_is_section_unfolded(get_edited_property())) {
			if (!sub_inspector) {
				sub_inspector = memnew(EditorInspector);
				sub_inspector->set_vertical_scroll_mode(ScrollContainer::SCROLL_MODE_DISABLED);
				sub_inspector->set_use_doc_hints(true);
				sub_inspector->set_sub_inspector(true);
				sub_inspector->set_property_name_style(InspectorDock::get_singleton()->get_property_name_style());
				sub_inspector->connect("property_keyed", callable_mp(this, &EditorPropertyResource::_sub_inspector_property_keyed));
				sub_inspector->connect("resource_selected", callable_mp(this, &EditorPropertyResource::_sub_inspector_resource_selected));
				sub_inspector->connect("object_id_selected", callable_mp(this, &EditorPropertyResource::_sub_inspector_object_id_selected));
				sub_inspector->set_keying(is_keying());
				sub_inspector->set_read_only(is_read_only());
				sub_inspector->set_use_folding(is_using_folding());
				sub_inspector_vbox = memnew(VBoxContainer);
				add_child(sub_inspector_vbox);
				set_bottom_editor(sub_inspector_vbox);
				sub_inspector_vbox->add_child(sub_inspector);
				resource_picker->set_toggle_pressed(true);
				Array editor_list;
				for (int i = 0; i < EditorNode::get_editor_data().get_editor_plugin_count(); i++) {
					EditorPlugin *ep = EditorNode::get_editor_data().get_editor_plugin(i);
					if (ep->handles(res.ptr())) {