### 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)

value_type = subtype;
			}
			if (value_type == Variant::OBJECT && Object::cast_to<EncodedObjectAsID>(value)) {
				EditorPropertyObjectID *editor = memnew(EditorPropertyObjectID);
				editor->setup("Object");
				prop = editor;
			} else {
				prop = EditorInspector::instantiate_property_editor(nullptr, value_type, "", subtype_hint, subtype_hint_string, PROPERTY_USAGE_NONE);
			}
			prop->set_object_and_property(object.ptr(), prop_name);
			prop->set_label(itos(i + offset));
			prop->set_selectable(false);
			prop->set_use_folding(is_using_folding());
			prop->connect("property_changed", callable_mp(this, &EditorPropertyArray::_property_changed));
			prop->connect("object_id_selected", callable_mp(this, &EditorPropertyArray::_object_id_selected));
			prop->set_h_size_flags(SIZE_EXPAND_FILL);
			prop->set_read_only(is_read_only());
			hbox->add_child(prop);
			bool is_untyped_array = array.get_type() == Variant::ARRAY && subtype == Variant::NIL;
			if (is_untyped_array) {
				Button *edit_btn = memnew(Button);
				edit_btn->set_icon(get_theme_icon(SNAME("Edit"), SNAME("EditorIcons")));
				hbox->add_child(edit_btn);
				edit_btn->set_disabled(is_read_only());
				edit_btn->connect("pressed", callable_mp(this, &EditorPropertyArray::_change_type).bind(edit_btn, i + offset));
			} else {
				Button *remove_btn = memnew(Button);
				remove_btn->set_icon(get_theme_icon(SNAME("Remove"), SNAME("EditorIcons")));
				remove_btn->set_disabled(is_read_only());
				remove_btn->connect("pressed", callable_mp(this, &EditorPropertyArray::_remove_pressed).bind(i + offset));