### 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 (reorder_from_index < 0 || is_read_only()) {
		return;
	}
	Ref<InputEventMouseMotion> mm = p_event;
	if (mm.is_valid()) {
		Variant array = object->get_array();
		int size = array.call("size");
		
		reorder_mouse_y_delta += mm->get_relative().y;
		
		
		if ((reorder_to_index == 0 && reorder_mouse_y_delta < 0.0f) || (reorder_to_index == size - 1 && reorder_mouse_y_delta > 0.0f)) {
			reorder_mouse_y_delta = 0.0f;