### 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_COND(!p_dictionary.has("names"));
	ERR_FAIL_COND(!p_dictionary.has("variants"));
	ERR_FAIL_COND(!p_dictionary.has("node_count"));
	ERR_FAIL_COND(!p_dictionary.has("nodes"));
	ERR_FAIL_COND(!p_dictionary.has("conn_count"));
	ERR_FAIL_COND(!p_dictionary.has("conns"));
	
	int version = 1;
	if (p_dictionary.has("version")) {
		version = p_dictionary["version"];
	}
	ERR_FAIL_COND_MSG(version > PACKED_SCENE_VERSION, "Save format version too new.");
	const int node_count = p_dictionary["node_count"];
	const Vector<int> snodes = p_dictionary["nodes"];
	ERR_FAIL_COND(snodes.size() < node_count);
	const int conn_count = p_dictionary["conn_count"];
	const Vector<int> sconns = p_dictionary["conns"];
	ERR_FAIL_COND(sconns.size() < conn_count);
	Vector<String> snames = p_dictionary["names"];
	if (snames.size()) {
		int namecount = snames.size();
		names.resize(namecount);
		const String *r = snames.ptr();
		for (int i = 0; i < names.size(); i++) {