Output of `optimizing` does not return the number of used iterations or reason why the optimization was terminated

It would be great if the output of optimizing contained the number of iterations the optimizer ran. This could be then to check whether the optimization terminated because of hitting the maximum number of iterations. Even better solution would be to get the actual reason for the termination from the output, which is currently only available in the print when verbose = TRUE, but I understand that this is likely more difficult due to the way rstan works.

Example

library(rstan)
m <- stan_model(
  model_code = "
  transformed data {
    vector[2] y = [5, 10.2]';
  } 
  parameters {
    real x;
  } 
  model {
    y ~ normal(x, 1);
  }")
f <- optimizing(m, iter = 2, verbose = TRUE)
str(f)
Chain 1: Initial log joint probability = -38.2441
Chain 1:     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
Chain 1:        1      -26.9098       1.12221       8.97772         0.1       0.001        4   
Chain 1:     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes 
Chain 1:        2         -6.76       4.48886   7.10543e-15           1           1        5   
Chain 1: Optimization terminated normally: 
Chain 1:   Convergence detected: gradient norm is below tolerance

str(f)
List of 4
 $ par        : Named num 7.6
  ..- attr(*, "names")= chr "x"
 $ value      : num -6.76
 $ return_code: int 0
 $ theta_tilde: num [1, 1] 7.6
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr "x"

RStan Version:

2.32.6

R Version:

4.3.0

Operating System:

Windows 10

Start at the optimizing() entry point and compare its returned list with the verbose termination output shown in the example. Done means the result exposes the optimizer's iteration count and, if feasible, the termination reason, with behavior represented in the existing optimizing() tests.