### 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)

List<Node *> stray_instances;
#define NODE_FROM_ID(p_name, p_id)                      \
	Node *p_name;                                       \
	if (p_id & FLAG_ID_IS_PATH) {                       \
		NodePath np = node_paths[p_id & FLAG_MASK];     \
		p_name = ret_nodes[0]->get_node_or_null(np);    \
	} else {                                            \
		ERR_FAIL_INDEX_V(p_id &FLAG_MASK, nc, nullptr); \
		p_name = ret_nodes[p_id & FLAG_MASK];           \
	}
	int nc = nodes.size();
	ERR_FAIL_COND_V(nc == 0, nullptr);
	const StringName *snames = nullptr;
	int sname_count = names.size();
	if (sname_count) {
		snames = &names[0];
	}
	const Variant *props = nullptr;
	int prop_count = variants.size();
	if (prop_count) {
		props = &variants[0];
	}