### 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->set(prop_name, prop_variant);
								continue;
							}
							const Array &array = prop_variant;
							for (int k = 0; k < array.size(); k++) {
								DeferredNodePathProperties dnp;
								dnp.path = array[k];
								dnp.base = node;
								
								dnp.property = String(prop_name) + "/indices/" + itos(k);
								deferred_node_paths.push_back(dnp);
							}
						} else {
							node->set(PackedScene::META_POINTER_PROPERTY_BASE + String(prop_name), prop_variant);
							if (!Engine::get_singleton()->is_editor_hint()) {
								
								DeferredNodePathProperties dnp;
								dnp.path = prop_variant;
								dnp.base = node;
								dnp.property = prop_name;
								deferred_node_paths.push_back(dnp);
							}
						}
						continue;
					}
					ERR_FAIL_INDEX_V(nprops[j].name, sname_count, nullptr);
					if (snames[nprops[j].name] == CoreStringNames::get_singleton()->_script) {