### 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 = Array(set_array, get_array.get_typed_builtin(), get_array.get_typed_class_name(), get_array.get_typed_script());
								}
							}
						}
						if (p_edit_state == GEN_EDIT_STATE_INSTANCE && value.get_type() != Variant::OBJECT) {
							value = value.duplicate(true); 
						}
						bool set_valid = true;
						if (ResourceLoader::is_creating_missing_resources_if_class_unavailable_enabled() && value.get_type() == Variant::OBJECT) {
							Ref<MissingResource> mr = value;
							if (mr.is_valid()) {
								missing_resource_properties[snames[nprops[j].name]] = mr;
								set_valid = false;
							}
						}
						if (set_valid) {
							node->set(snames[nprops[j].name], value, &valid);
						}
					}
				}
				if (!missing_resource_properties.is_empty()) {
					node->set_meta(META_MISSING_RESOURCES, missing_resource_properties);
				}
			}
			
			
			for (int j = 0; j < n.groups.size(); j++) {
				ERR_FAIL_INDEX_V(n.groups[j], sname_count, nullptr);
				node->add_to_group(snames[n.groups[j]], true);
			}