### 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
save_all_scenes();
	ProjectSettings::get_singleton()->save();
	disk_changed->hide();
}
void EditorNode::_reload_modified_scenes() {
	int current_idx = editor_data.get_edited_scene();
	for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
		if (editor_data.get_scene_path(i) == "") {
			continue;
		}
		uint64_t last_date = editor_data.get_scene_modified_time(i);
		uint64_t date = FileAccess::get_modified_time(editor_data.get_scene_path(i));
		if (date > last_date) {
			String filename = editor_data.get_scene_path(i);
			editor_data.set_edited_scene(i);
			_remove_edited_scene(false);
			Error err = load_scene(filename, false, false, true, false, true);
			if (err != OK) {
				ERR_PRINT(vformat("Failed to load scene: %s", filename));
			}
			editor_data.move_edited_scene_to_index(i);
		}
	}
	_set_current_scene(current_idx);
	scene_tabs->update_scene_tabs();
	disk_changed->hide();
}
void EditorNode::_reload_project_settings() {