### 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
{
		String path = p_resource->get_path();
		if (!path.is_resource_file()) {
			int srpos = path.find("::");
			if (srpos != -1) {
				String base = path.substr(0, srpos);
				if (!get_edited_scene() || get_edited_scene()->get_scene_file_path() != base) {
					show_warning(TTR("This resource can't be saved because it does not belong to the edited scene. Make it unique first."));
					return;
				}
			}
		} else if (FileAccess::exists(path + ".import")) {
			show_warning(TTR("This resource can't be saved because it was imported from another file. Make it unique first."));
			return;