### 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)

ERR_FAIL_INDEX_V(p_idx, nodes.size(), NodePath());
	if (nodes[p_idx].parent < 0 || nodes[p_idx].parent == NO_PARENT_SAVED) {
		if (p_for_parent) {
			return NodePath();
		} else {
			return NodePath(".");
		}
	}
	Vector<StringName> sub_path;
	NodePath base_path;
	int nidx = p_idx;
	while (true) {
		if (nodes[nidx].parent == NO_PARENT_SAVED || nodes[nidx].parent < 0) {
			sub_path.insert(0, ".");
			break;
		}
		if (!p_for_parent || p_idx != nidx) {
			sub_path.insert(0, names[nodes[nidx].name]);
		}
		if (nodes[nidx].parent & FLAG_ID_IS_PATH) {
			base_path = node_paths[nodes[nidx].parent & FLAG_MASK];
			break;
		} else {
			nidx = nodes[nidx].parent & FLAG_MASK;
		}
	}
	for (int i = base_path.get_name_count() - 1; i >= 0; i--) {
		sub_path.insert(0, base_path.get_name(i));
	}
	if (sub_path.is_empty()) {