### 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)

node->_acquire_unique_name_in_owner();
					}
				}
			}
			
			if (p_edit_state == GEN_EDIT_STATE_MAIN) {
				_sanitize_node_pinned_properties(node);
			} else {
				node->remove_meta("_edit_pinned_properties_");
			}
		}
		if (missing_node) {
			missing_node->set_recording_properties(false);
		}
		ret_nodes[i] = node;
		if (node && gen_node_path_cache && ret_nodes[0]) {
			NodePath n2 = ret_nodes[0]->get_path_to(node);
			node_path_cache[n2] = i;
		}
	}
	for (const DeferredNodePathProperties &dnp : deferred_node_paths) {
		
		Node *other = dnp.base->get_node_or_null(dnp.path);
		const String string_property = dnp.property;
		if (string_property.contains("/indices/")) {
			
			const String base_property = string_property.get_slice("/", 0);
			const int index = string_property.get_slice("/", 2).to_int();
			Array array = dnp.base->get(base_property);
			if (array.size() >= index) {