### 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)

}
void EditorPropertyQuaternion::setup(double p_min, double p_max, double p_step, bool p_hide_slider, const String &p_suffix, bool p_hide_editor) {
	for (int i = 0; i < 4; i++) {
		spin[i]->set_min(p_min);
		spin[i]->set_max(p_max);
		spin[i]->set_step(p_step);
		spin[i]->set_hide_slider(p_hide_slider);
		spin[i]->set_allow_greater(true);
		spin[i]->set_allow_lesser(true);
		
		
		spin[i]->set_suffix(p_suffix);
	}
	for (int i = 0; i < 3; i++) {
		euler[i]->set_min(-360);
		euler[i]->set_max(360);
		euler[i]->set_step(0.1);
		euler[i]->set_hide_slider(false);
		euler[i]->set_allow_greater(true);
		euler[i]->set_allow_lesser(true);
		euler[i]->set_suffix(U"\u00B0");
	}
	if (p_hide_editor) {
		edit_button->hide();
	}
}
EditorPropertyQuaternion::EditorPropertyQuaternion() {