### 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)

size_slider->set_max(INT32_MAX);
			size_slider->set_h_size_flags(SIZE_EXPAND_FILL);
			size_slider->set_read_only(is_read_only());
			size_slider->connect("value_changed", callable_mp(this, &EditorPropertyArray::_length_changed));
			hbox->add_child(size_slider);
			property_vbox = memnew(VBoxContainer);
			property_vbox->set_h_size_flags(SIZE_EXPAND_FILL);
			vbox->add_child(property_vbox);
			button_add_item = EditorInspector::create_inspector_action_button(TTR("Add Element"));
			button_add_item->set_icon(get_theme_icon(SNAME("Add"), SNAME("EditorIcons")));
			button_add_item->connect(SNAME("pressed"), callable_mp(this, &EditorPropertyArray::_add_element));
			button_add_item->set_disabled(is_read_only());
			vbox->add_child(button_add_item);
			paginator = memnew(EditorPaginator);
			paginator->connect("page_changed", callable_mp(this, &EditorPropertyArray::_page_changed));
			vbox->add_child(paginator);
		} else {
			
			for (int i = property_vbox->get_child_count() - 1; i >= 0; i--) {
				Node *child = property_vbox->get_child(i);
				if (child == reorder_selected_element_hbox) {
					continue; 
				}
				child->queue_free(); 
				property_vbox->remove_child(child);
			}
		}
		size_slider->set_value(size);
		property_vbox->set_visible(size > 0);
		button_add_item->set_visible(page_index == max_page);