### 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
_reset_animation_mixers(scene, &anim_backups);
	save_default_environment();
	_save_editor_states(p_file, idx);
	Ref<PackedScene> sdata;
	if (ResourceCache::has(p_file)) {
		
		
		
		sdata = ResourceCache::get_ref(p_file);
		if (sdata.is_valid()) {
			sdata->recreate_state();
		} else {
			sdata.instantiate();
		}
	} else {
		sdata.instantiate();
	}
	Error err = sdata->pack(scene);
	if (err != OK) {
		show_accept(TTR("Couldn't save scene. Likely dependencies (instances or inheritance) couldn't be satisfied."), TTR("OK"));
		return;
	}
	int flg = 0;
	if (EDITOR_GET("filesystem/on_save/compress_binary_resources")) {
		flg |= ResourceSaver::FLAG_COMPRESS;
	}
	flg |= ResourceSaver::FLAG_REPLACE_SUBRESOURCE_PATHS;
	err = ResourceSaver::save(sdata, p_file, flg);
	
	emit_signal(SNAME("scene_saved"), p_file);