Peter, you're right, the city-by-city list of lounges does show the Singapore Air lounges, and the Star Alliance site doesn't show the newest members yet.
But -- SQ has been in since 1999 and it shows as a member, so it's clearly been added to the current site, and yet none of its lounges show as available for status and F fliers on other airlines. So either *A is
way behind, or its other members think that it's hopeless to get into an SQ lounge.