### 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)

EditorPropertyRangeHint hint = _parse_range_hint(p_hint, p_hint_text, 1, true);
				editor->setup(hint.min, hint.max, hint.step, hint.hide_slider, hint.or_greater, hint.or_less, hint.suffix);
				return editor;
			}
		} break;
		case Variant::FLOAT: {
			if (p_hint == PROPERTY_HINT_EXP_EASING) {
				EditorPropertyEasing *editor = memnew(EditorPropertyEasing);
				bool positive_only = false;
				bool flip = false;
				const Vector<String> hints = p_hint_text.split(",");
				for (int i = 0; i < hints.size(); i++) {
					const String hint = hints[i].strip_edges();
					if (hint == "attenuation") {
						flip = true;
					}
					if (hint == "positive_only") {
						positive_only = true;
					}
				}
				editor->setup(positive_only, flip);
				return editor;
			} else {
				EditorPropertyFloat *editor = memnew(EditorPropertyFloat);
				EditorPropertyRangeHint hint = _parse_range_hint(p_hint, p_hint_text, default_float_step);
				editor->setup(hint.min, hint.max, hint.step, hint.hide_slider, hint.exp_range, hint.or_greater, hint.or_less, hint.suffix, hint.radians);
				return editor;
			}
		} break;
		case Variant::STRING: {