### 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)

d["variants"] = variants;
	Vector<int> rnodes;
	d["node_count"] = nodes.size();
	for (int i = 0; i < nodes.size(); i++) {
		const NodeData &nd = nodes[i];
		rnodes.push_back(nd.parent);
		rnodes.push_back(nd.owner);
		rnodes.push_back(nd.type);
		uint32_t name_index = nd.name;
		if (nd.index < (1 << (32 - NAME_INDEX_BITS)) - 1) { 
			name_index |= uint32_t(nd.index + 1) << NAME_INDEX_BITS; 
		}
		rnodes.push_back(name_index);
		rnodes.push_back(nd.instance);
		rnodes.push_back(nd.properties.size());
		for (int j = 0; j < nd.properties.size(); j++) {
			rnodes.push_back(nd.properties[j].name);
			rnodes.push_back(nd.properties[j].value);
		}
		rnodes.push_back(nd.groups.size());
		for (int j = 0; j < nd.groups.size(); j++) {
			rnodes.push_back(nd.groups[j]);
		}
	}
	d["nodes"] = rnodes;
	Vector<int> rconns;
	d["conn_count"] = connections.size();
	for (int i = 0; i < connections.size(); i++) {
		const ConnectionData &cd = connections[i];
		rconns.push_back(cd.from);