### 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 (read_only) {
		return;
	}
	const Ref<InputEventMouseMotion> mm = p_ev;
	if (mm.is_valid()) {
		_update_hovered(mm->get_position());
		return;
	}
	const Ref<InputEventMouseButton> mb = p_ev;
	if (mb.is_valid() && mb->get_button_index() == MouseButton::LEFT && mb->is_pressed()) {
		_update_hovered(mb->get_position());
		_update_flag();
	}
	if (mb.is_valid() && mb->get_button_index() == MouseButton::RIGHT && mb->is_pressed()) {
		if (hovered_index >= 0) {
			renamed_layer_index = hovered_index;
			layer_rename->set_position(get_screen_position() + mb->get_position());
			layer_rename->reset_size();
			layer_rename->popup();
		}
	}
}
void EditorPropertyLayersGrid::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_DRAW: {
			Size2 grid_size = get_grid_size();
			grid_size.x = get_size().x;
			flag_rects.clear();