### 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)

value = missing_resource_properties[E.name];
			}
		} else if (E.type == Variant::ARRAY && E.hint == PROPERTY_HINT_TYPE_STRING) {
			int hint_subtype_separator = E.hint_string.find(":");
			if (hint_subtype_separator >= 0) {
				String subtype_string = E.hint_string.substr(0, hint_subtype_separator);
				int slash_pos = subtype_string.find("/");
				PropertyHint subtype_hint = PropertyHint::PROPERTY_HINT_NONE;
				if (slash_pos >= 0) {
					subtype_hint = PropertyHint(subtype_string.get_slice("/", 1).to_int());
					subtype_string = subtype_string.substr(0, slash_pos);
				}
				Variant::Type subtype = Variant::Type(subtype_string.to_int());
				use_deferred_node_path_bit = subtype == Variant::OBJECT && subtype_hint == PROPERTY_HINT_NODE_TYPE;
			}
		}
		if (!pinned_props.has(name)) {
			bool is_valid_default = false;
			Variant default_value = PropertyUtils::get_property_default_value(p_node, name, &is_valid_default, &states_stack, true);
			if (is_valid_default && !PropertyUtils::is_property_value_different(value, default_value)) {
				continue;
			}
		}
		NodeData::Property prop;
		prop.name = _nm_get_string(name, name_map);
		prop.value = _vm_get_variant(value, variant_map);
		if (use_deferred_node_path_bit) {
			prop.name |= FLAG_PATH_PROPERTY_IS_NODE;
		}
		nd.properties.push_back(prop);