### 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
Viewport::SDFOversize sdf_oversize = Viewport::SDFOversize(int(GLOBAL_GET("rendering/2d/sdf/oversize")));
	scene_root->set_sdf_oversize(sdf_oversize);
	Viewport::SDFScale sdf_scale = Viewport::SDFScale(int(GLOBAL_GET("rendering/2d/sdf/scale")));
	scene_root->set_sdf_scale(sdf_scale);
	Viewport::MSAA msaa = Viewport::MSAA(int(GLOBAL_GET("rendering/anti_aliasing/quality/msaa_2d")));
	scene_root->set_msaa_2d(msaa);
	bool use_hdr_2d = GLOBAL_GET("rendering/viewport/hdr_2d");
	scene_root->set_use_hdr_2d(use_hdr_2d);
	float mesh_lod_threshold = GLOBAL_GET("rendering/mesh_lod/lod_change/threshold_pixels");
	scene_root->set_mesh_lod_threshold(mesh_lod_threshold);
	RS::get_singleton()->decals_set_filter(RS::DecalFilter(int(GLOBAL_GET("rendering/textures/decals/filter"))));
	RS::get_singleton()->light_projectors_set_filter(RS::LightProjectorFilter(int(GLOBAL_GET("rendering/textures/light_projectors/filter"))));
	SceneTree *tree = get_tree();
	tree->set_debug_collisions_color(GLOBAL_GET("debug/shapes/collision/shape_color"));
	tree->set_debug_collision_contact_color(GLOBAL_GET("debug/shapes/collision/contact_color"));
	ResourceImporterTexture::get_singleton()->update_imports();
#ifdef DEBUG_ENABLED
	NavigationServer3D::get_singleton()->set_debug_navigation_edge_connection_color(GLOBAL_GET("debug/shapes/navigation/edge_connection_color"));
	NavigationServer3D::get_singleton()->set_debug_navigation_geometry_edge_color(GLOBAL_GET("debug/shapes/navigation/geometry_edge_color"));
	NavigationServer3D::get_singleton()->set_debug_navigation_geometry_face_color(GLOBAL_GET("debug/shapes/navigation/geometry_face_color"));
	NavigationServer3D::get_singleton()->set_debug_navigation_geometry_edge_disabled_color(GLOBAL_GET("debug/shapes/navigation/geometry_edge_disabled_color"));
	NavigationServer3D::get_singleton()->set_debug_navigation_geometry_face_disabled_color(GLOBAL_GET("debug/shapes/navigation/geometry_face_disabled_color"));
	NavigationServer3D::get_singleton()->set_debug_navigation_enable_edge_connections(GLOBAL_GET("debug/shapes/navigation/enable_edge_connections"));
	NavigationServer3D::get_singleton()->set_debug_navigation_enable_edge_connections_xray(GLOBAL_GET("debug/shapes/navigation/enable_edge_connections_xray"));
	NavigationServer3D::get_singleton()->set_debug_navigation_enable_edge_lines(GLOBAL_GET("debug/shapes/navigation/enable_edge_lines"));
	NavigationServer3D::get_singleton()->set_debug_navigation_enable_edge_lines_xray(GLOBAL_GET("debug/shapes/navigation/enable_edge_lines_xray"));
	NavigationServer3D::get_singleton()->set_debug_navigation_enable_geometry_face_random_color(GLOBAL_GET("debug/shapes/navigation/enable_geometry_face_random_color"));
#endif 
}
void EditorNode::_gdextensions_reloaded() {