### 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)

String prop_name;
			Variant key;
			Variant value;
			if (i < amount) {
				prop_name = "indices/" + itos(i + offset);
				key = dict.get_key_at_index(i + offset);
				value = dict.get_value_at_index(i + offset);
			} else if (i == amount) {
				prop_name = "new_item_key";
				value = object->get_new_item_key();
			} else if (i == amount + 1) {
				prop_name = "new_item_value";
				value = object->get_new_item_value();
			}
			EditorProperty *prop = nullptr;
			switch (value.get_type()) {
				case Variant::NIL: {
					prop = memnew(EditorPropertyNil);
				} break;
				
				case Variant::BOOL: {
					prop = memnew(EditorPropertyCheck);
				} break;
				case Variant::INT: {
					EditorPropertyInteger *editor = memnew(EditorPropertyInteger);
					editor->setup(-100000, 100000, 1, false, true, true);
					prop = editor;
				} break;
				case Variant::FLOAT: {
					EditorPropertyFloat *editor = memnew(EditorPropertyFloat);