### 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)

int64_t val = get_edited_property_value();
	setting = true;
	spin->set_value(val);
	setting = false;
#ifdef DEBUG_ENABLED
	
	if (val != (int64_t)(double)(val)) {
		WARN_PRINT("Cannot reliably represent '" + itos(val) + "' in the inspector, value is too large.");
	}
#endif
}
void EditorPropertyInteger::_bind_methods() {
}
void EditorPropertyInteger::setup(int64_t p_min, int64_t p_max, int64_t p_step, bool p_hide_slider, bool p_allow_greater, bool p_allow_lesser, const String &p_suffix) {
	spin->set_min(p_min);
	spin->set_max(p_max);
	spin->set_step(p_step);
	spin->set_hide_slider(p_hide_slider);
	spin->set_allow_greater(p_allow_greater);
	spin->set_allow_lesser(p_allow_lesser);
	spin->set_suffix(p_suffix);
}
EditorPropertyInteger::EditorPropertyInteger() {
	spin = memnew(EditorSpinSlider);
	spin->set_flat(true);
	add_child(spin);
	add_focusable(spin);
	spin->connect("value_changed", callable_mp(this, &EditorPropertyInteger::_value_changed));
}
void EditorPropertyObjectID::_set_read_only(bool p_read_only) {