### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
for (int i = p_start; i < editor_data.get_edited_scene_count(); i++) {
		if (!editor_data.get_edited_scene_root(i)) {
			continue;
		}
		String scene_filename = editor_data.get_edited_scene_root(i)->get_scene_file_path();
		if (p_valid_filename && scene_filename.is_empty()) {
			continue;
		}
		bool unsaved = EditorUndoRedoManager::get_singleton()->is_history_unsaved(editor_data.get_scene_history_id(i));
		if (unsaved) {
			return i;
		} else {
			for (int j = 0; j < editor_data.get_editor_plugin_count(); j++) {
				if (!editor_data.get_editor_plugin(j)->get_unsaved_status(scene_filename).is_empty()) {
					return i;
				}
			}
		}
	}
	return -1;
}
void EditorNode::_exit_editor(int p_exit_code) {