### 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)

}
EditorPropertyMultilineText::EditorPropertyMultilineText(bool p_expression) {
	HBoxContainer *hb = memnew(HBoxContainer);
	hb->add_theme_constant_override("separation", 0);
	add_child(hb);
	set_bottom_editor(hb);
	text = memnew(TextEdit);
	text->connect("text_changed", callable_mp(this, &EditorPropertyMultilineText::_text_changed));
	text->set_line_wrapping_mode(TextEdit::LineWrappingMode::LINE_WRAPPING_BOUNDARY);
	add_focusable(text);
	hb->add_child(text);
	text->set_h_size_flags(SIZE_EXPAND_FILL);
	open_big_text = memnew(Button);
	open_big_text->set_flat(true);
	open_big_text->connect("pressed", callable_mp(this, &EditorPropertyMultilineText::_open_big_text));
	hb->add_child(open_big_text);
	big_text_dialog = nullptr;
	big_text = nullptr;
	if (p_expression) {
		expression = true;
		Ref<EditorStandardSyntaxHighlighter> highlighter;
		highlighter.instantiate();
		text->set_syntax_highlighter(highlighter);
	}
}
void EditorPropertyTextEnum::_set_read_only(bool p_read_only) {