### 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)

names.write[i] = r[i];
		}
	}
	Array svariants = p_dictionary["variants"];
	if (svariants.size()) {
		int varcount = svariants.size();
		variants.resize(varcount);
		for (int i = 0; i < varcount; i++) {
			variants.write[i] = svariants[i];
		}
	} else {
		variants.clear();
	}
	nodes.resize(node_count);
	if (node_count) {
		const int *r = snodes.ptr();
		int idx = 0;
		for (int i = 0; i < node_count; i++) {
			NodeData &nd = nodes.write[i];
			nd.parent = r[idx++];
			nd.owner = r[idx++];
			nd.type = r[idx++];
			uint32_t name_index = r[idx++];
			nd.name = name_index & ((1 << NAME_INDEX_BITS) - 1);
			nd.index = (name_index >> NAME_INDEX_BITS);
			nd.index--; 
			nd.instance = r[idx++];
			nd.properties.resize(r[idx++]);
			for (int j = 0; j < nd.properties.size(); j++) {
				nd.properties.write[j].name = r[idx++];