### 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)

} else if (slice == "hide_slider") {
				hint.hide_slider = true;
			} else if (slice == "exp") {
				hint.exp_range = true;
			}
		}
	}
	bool degrees = false;
	for (int i = 0; i < slices.size(); i++) {
		String slice = slices[i].strip_edges();
		if (slice == "radians") {
			hint.radians = true;
		} else if (slice == "degrees") {
			degrees = true;
		} else if (slice.begins_with("suffix:")) {
			hint.suffix = " " + slice.replace_first("suffix:", "").strip_edges();
		}
	}
	if ((hint.radians || degrees) && hint.suffix.is_empty()) {
		hint.suffix = U"\u00B0";
	}
	ERR_FAIL_COND_V_MSG(hint.step == 0, hint,
			vformat("Invalid PROPERTY_HINT_RANGE with hint \"%s\": Step cannot be 0.", p_hint_text));
	return hint;
}
EditorProperty *EditorInspectorDefaultPlugin::get_editor_for_property(Object *p_object, const Variant::Type p_type, const String &p_path, const PropertyHint p_hint, const String &p_hint_text, const BitField<PropertyUsageFlags> p_usage, const bool p_wide) {
	double default_float_step = EDITOR_GET("interface/inspector/default_float_step");
	switch (p_type) {
		
		case Variant::NIL: {