Can syphills be transmitted by contact with sperm from a sink? such as touching or accidentally drinking sink water with sperm in it?

possible I suppose. But unlikely. You need to Bev infected by spirochete. I would Google spirochete survival in sink. Someone must have studied. Also go to uptodate.com and CDC.gov and search.

No. Syphilis cannot be contracted in that fashion.

No. Contracting a syphilis is almost always through direct sexual contact with ulcerative lesions (small open wounds) of the skin or mucous membranes of infected people.

Would totally agree that surface contact is NOT a vector for syphilis infectivity, and doubt the infective spirochete would survive in a sink.