I think the transition actually happens midway between 28th and Valley; San Jose Ave (the named thing, not the paved road) continues straight NNE towards the hospital, with the name switching from the divided 4-lane roadway to the unmarked 1-lane cycleway/parking path; the transition is barricaded off to cars but passable to foot and cycle traffic at the southern apex of the little triangular park.

Thinking about it more, my guess would be that the original San Jose Ave was always straight NNE/SSW, and when Guerrero was widened and became the main connector to the Caltrans-owned 280 approach, the physical paving was redone to eliminate that intersection and make the 4-lane approach one contiguous roadway.

I'll see if I can dig up the SF Assessor's survey maps to confirm any of that.