### 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)

if (p_hint == PROPERTY_HINT_ENUM || p_hint == PROPERTY_HINT_ENUM_SUGGESTION) {
				EditorPropertyTextEnum *editor = memnew(EditorPropertyTextEnum);
				Vector<String> options = p_hint_text.split(",", false);
				editor->setup(options, false, (p_hint == PROPERTY_HINT_ENUM_SUGGESTION));
				return editor;
			} else if (p_hint == PROPERTY_HINT_MULTILINE_TEXT) {
				EditorPropertyMultilineText *editor = memnew(EditorPropertyMultilineText);
				return editor;
			} else if (p_hint == PROPERTY_HINT_EXPRESSION) {
				EditorPropertyMultilineText *editor = memnew(EditorPropertyMultilineText(true));
				return editor;
			} else if (p_hint == PROPERTY_HINT_TYPE_STRING) {
				EditorPropertyClassName *editor = memnew(EditorPropertyClassName);
				editor->setup("Object", p_hint_text);
				return editor;
			} else if (p_hint == PROPERTY_HINT_LOCALE_ID) {
				EditorPropertyLocale *editor = memnew(EditorPropertyLocale);
				editor->setup(p_hint_text);
				return editor;
			} else if (p_hint == PROPERTY_HINT_DIR || p_hint == PROPERTY_HINT_FILE || p_hint == PROPERTY_HINT_SAVE_FILE || p_hint == PROPERTY_HINT_GLOBAL_SAVE_FILE || p_hint == PROPERTY_HINT_GLOBAL_DIR || p_hint == PROPERTY_HINT_GLOBAL_FILE) {
				Vector<String> extensions = p_hint_text.split(",");
				bool global = p_hint == PROPERTY_HINT_GLOBAL_DIR || p_hint == PROPERTY_HINT_GLOBAL_FILE || p_hint == PROPERTY_HINT_GLOBAL_SAVE_FILE;
				bool folder = p_hint == PROPERTY_HINT_DIR || p_hint == PROPERTY_HINT_GLOBAL_DIR;
				bool save = p_hint == PROPERTY_HINT_SAVE_FILE || p_hint == PROPERTY_HINT_GLOBAL_SAVE_FILE;
				EditorPropertyPath *editor = memnew(EditorPropertyPath);
				editor->setup(extensions, folder, global);
				if (save) {
					editor->set_save_mode();
				}
				return editor;