### 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)

uint32_t value = get_edited_property_value();
	for (int i = 0; i < flags.size(); i++) {
		flags[i]->set_pressed((value & flag_values[i]) == flag_values[i]);
	}
}
void EditorPropertyFlags::setup(const Vector<String> &p_options) {
	ERR_FAIL_COND(flags.size());
	bool first = true;
	uint32_t current_val;
	for (int i = 0; i < p_options.size(); i++) {
		
		String option = p_options[i].strip_edges();
		if (option.is_empty()) {
			continue;
		}
		const int flag_index = flags.size(); 
		
		Vector<String> text_split = p_options[i].split(":");
		if (text_split.size() != 1) {
			current_val = text_split[1].to_int();
		} else {
			current_val = 1 << i;
		}
		flag_values.push_back(current_val);
		
		CheckBox *cb = memnew(CheckBox);
		cb->set_text(option);
		cb->set_clip_text(true);