### 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)

case LAYER_NAVIGATION_3D: {
			basename = "layer_names/3d_navigation";
			layer_group_size = 4;
			layer_count = 32;
		} break;
		case LAYER_AVOIDANCE: {
			basename = "layer_names/avoidance";
			layer_group_size = 4;
			layer_count = 32;
		} break;
	}
	Vector<String> names;
	Vector<String> tooltips;
	for (int i = 0; i < layer_count; i++) {
		String name;
		if (ProjectSettings::get_singleton()->has_setting(basename + vformat("/layer_%d", i + 1))) {
			name = GLOBAL_GET(basename + vformat("/layer_%d", i + 1));
		}
		if (name.is_empty()) {
			name = vformat(TTR("Layer %d"), i + 1);
		}
		names.push_back(name);
		tooltips.push_back(name + "\n" + vformat(TTR("Bit %d, value %d"), i, 1 << i));
	}
	grid->names = names;
	grid->tooltips = tooltips;
	grid->layer_group_size = layer_group_size;
	grid->layer_count = layer_count;
}
void EditorPropertyLayers::set_layer_name(int p_index, const String &p_name) {