Hi! Welcome to the Stan forum!
I’m not into survival models, but I think quite a few people on this Forum ar (maybe I can tag them later).
Did you get warnings about divergent transitions? Or any other warnings?
This looks fishy. Did you try non-centered parameterization here? (The easiest is probably to write vector<multiplier=0,offset=sigma_S>[m] S in the paramteres block.)
Also, you could try with tighter priors on the sigmas (lognormal has a heavy tail).
(All of the above is assuming your model is correct, which I did not check, though.)
Cheers,
Max