### 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)

if (p_node != p_owner && p_node->get_owner() && p_node->get_owner() != p_owner && !p_owner->is_editable_instance(p_node->get_owner())) {
		return OK;
	}
	List<MethodInfo> _signals;
	p_node->get_signal_list(&_signals);
	_signals.sort();
	
	
	for (const MethodInfo &E : _signals) {
		List<Node::Connection> conns;
		p_node->get_signal_connection_list(E.name, &conns);
		conns.sort();
		for (const Node::Connection &F : conns) {
			const Node::Connection &c = F;
			if (!(c.flags & CONNECT_PERSIST)) { 
				continue;
			}
			
			
			Node *target = Object::cast_to<Node>(c.callable.get_object());
			if (!target) {
				continue;
			}
			Vector<Variant> binds;
			int unbinds = 0;
			Callable base_callable;
			if (c.callable.is_custom()) {
				CallableCustomBind *ccb = dynamic_cast<CallableCustomBind *>(c.callable.get_custom());