### 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)

bool horizontal = EDITOR_GET("interface/inspector/horizontal_vector_types_editing");
	VBoxContainer *bc = memnew(VBoxContainer);
	edit_custom_bc = memnew(VBoxContainer);
	BoxContainer *edit_custom_layout;
	if (horizontal) {
		default_layout = memnew(HBoxContainer);
		edit_custom_layout = memnew(HBoxContainer);
		set_bottom_editor(bc);
	} else {
		default_layout = memnew(VBoxContainer);
		edit_custom_layout = memnew(VBoxContainer);
	}
	edit_custom_bc->hide();
	add_child(bc);
	edit_custom_bc->set_h_size_flags(SIZE_EXPAND_FILL);
	default_layout->set_h_size_flags(SIZE_EXPAND_FILL);
	edit_custom_layout->set_h_size_flags(SIZE_EXPAND_FILL);
	bc->add_child(default_layout);
	bc->add_child(edit_custom_bc);
	static const char *desc[4] = { "x", "y", "z", "w" };
	for (int i = 0; i < 4; i++) {
		spin[i] = memnew(EditorSpinSlider);
		spin[i]->set_flat(true);