### 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)

}
EditorPropertyArray::EditorPropertyArray() {
	object.instantiate();
	page_length = int(EDITOR_GET("interface/inspector/max_array_dictionary_items_per_page"));
	edit = memnew(Button);
	edit->set_h_size_flags(SIZE_EXPAND_FILL);
	edit->set_clip_text(true);
	edit->connect("pressed", callable_mp(this, &EditorPropertyArray::_edit_pressed));
	edit->set_toggle_mode(true);
	SET_DRAG_FORWARDING_CD(edit, EditorPropertyArray);
	edit->connect("draw", callable_mp(this, &EditorPropertyArray::_button_draw));
	add_child(edit);
	add_focusable(edit);
	change_type = memnew(PopupMenu);
	add_child(change_type);
	change_type->connect("id_pressed", callable_mp(this, &EditorPropertyArray::_change_type_menu));
	changing_type_index = -1;
	subtype = Variant::NIL;
	subtype_hint = PROPERTY_HINT_NONE;
	subtype_hint_string = "";
}
void EditorPropertyDictionary::_property_changed(const String &p_property, Variant p_value, const String &p_name, bool p_changing) {