Hessian NaN with ordered_logistic_lpmf

I'm testing this via CmdStanR $hessian() method, but I guess the problem is in math.

$hessian() method works for the following Stan model if data y=2 but gives NaN if y=3. $laplace() method is able to compute finite Hessian (finite difference?), so the reason is not that Hessian would not exist (gradient is also close to 0, so the Hessian is computed (near) the mode).

data {
  int Y;
}
parameters {
  real mu;
}
model {
  target += ordered_logistic_lpmf(Y | mu, [-1, 1]');
  target += std_normal_lpdf(mu);
}

R code to reproduce

library(cmdstanr)
code_ordered <-
"data {
  int Y;
}
parameters {
  real mu;
}
model {
  target += ordered_logistic_lpmf(Y | mu, [-1, 1]');
  target += std_normal_lpdf(mu);
}
"
file_ordered <- write_stan_file(code_ordered)
model_ordered <- cmdstan_model(file_ordered,
                               compile_model_methods=TRUE,
                               compile_hessian_method=TRUE,
                               force_recompile=TRUE)
# This works
data_ordered <- list(Y = 2)
opt_ordered <- model_ordered$optimize(data = data_ordered, refresh=0)
opt_ordered$hessian(as.numeric(opt_ordered$unconstrain_draws(draws=opt_ordered$draws())))

# This works
lap_ordered <- model_ordered$laplace(data = data_ordered, refresh=0)
-1/var(lap_ordered$draws(variables="mu")) # Hessian from the draws

# This gives NaN
data_ordered <- list(Y = 3)
opt_ordered <- model_ordered$optimize(data = data_ordered, refresh=0);
opt_ordered$hessian(as.numeric(opt_ordered$unconstrain_draws(draws=opt_ordered$draws())))

# This works
lap_ordered <- model_ordered$laplace(data = data_ordered, refresh=0)
-1/var(lap_ordered$draws(variables="mu")) # Hessian from the draws

Reproduce the issue using the supplied Stan model and CmdStanR $hessian() calls, comparing Y=2 with Y=3 and the corresponding $laplace() results. Start by tracing the ordered_logistic_lpmf evaluation and Hessian path in the Stan Math code; done means identifying and correcting the NaN result while preserving finite Hessian behavior for both inputs.