### 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
Ref<CanvasItemMaterialConversionPlugin> canvas_item_mat_convert;
		canvas_item_mat_convert.instantiate();
		resource_conversion_plugins.push_back(canvas_item_mat_convert);
		Ref<ParticleProcessMaterialConversionPlugin> particles_mat_convert;
		particles_mat_convert.instantiate();
		resource_conversion_plugins.push_back(particles_mat_convert);
		Ref<ProceduralSkyMaterialConversionPlugin> procedural_sky_mat_convert;
		procedural_sky_mat_convert.instantiate();
		resource_conversion_plugins.push_back(procedural_sky_mat_convert);
		Ref<PanoramaSkyMaterialConversionPlugin> panorama_sky_mat_convert;
		panorama_sky_mat_convert.instantiate();
		resource_conversion_plugins.push_back(panorama_sky_mat_convert);
		Ref<PhysicalSkyMaterialConversionPlugin> physical_sky_mat_convert;
		physical_sky_mat_convert.instantiate();
		resource_conversion_plugins.push_back(physical_sky_mat_convert);
		Ref<FogMaterialConversionPlugin> fog_mat_convert;
		fog_mat_convert.instantiate();
		resource_conversion_plugins.push_back(fog_mat_convert);
		Ref<VisualShaderConversionPlugin> vshader_convert;
		vshader_convert.instantiate();
		resource_conversion_plugins.push_back(vshader_convert);
	}
	update_spinner_step_msec = OS::get_singleton()->get_ticks_msec();
	update_spinner_step_frame = Engine::get_singleton()->get_frames_drawn();
	editor_plugin_screen = nullptr;
	editor_plugins_over = memnew(EditorPluginList);
	editor_plugins_force_over = memnew(EditorPluginList);
	editor_plugins_force_input_forwarding = memnew(EditorPluginList);
	Ref<GDExtensionExportPlugin> gdextension_export_plugin;
	gdextension_export_plugin.instantiate();