### 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
List<String> scenes;
	int current_tab = scene_tabs->get_current_tab();
	for (int i = 0; i < p_resources.size(); i++) {
		String file_type = ResourceLoader::get_resource_type(p_resources[i]);
		if (file_type == "PackedScene") {
			scenes.push_back(p_resources[i]);
			
			continue;
		}
		if (!ResourceCache::has(p_resources[i])) {
			
			continue;
		}
		
		Ref<Resource> resource = ResourceCache::get_ref(p_resources[i]);
		if (resource.is_valid()) {
			resource->reload_from_file();
		}
	}
	
	AnimationPlayer *ap = AnimationPlayerEditor::get_singleton()->get_player();
	if (ap && scenes.size() > 0) {
		ap->stop(true);
	}
	for (const String &E : scenes) {