Provide access to initial values

We've recently discussed how CmdStan does not have a way to provide users access to the initial values it used:

• https://discourse.mc-stan.org/t/does-the-init-argument-work-with-cmdstanr/17255/19
• https://github.com/stan-dev/cmdstan/issues/918

It sounds like this is actually an io/services issue because the contents of a stan::io::var_context object would need to be dumped to text. Is that right?

I don't know how difficult this would be, but to me providing access to this information seems pretty important.

The most important information to convey to users I think would be inits for parameters on the constrained scale. Transformed parameters, generated quantities, and the unconstrained scale, are potentially useful but not as high of a priority.

Start by reading the linked CmdStan issue and Discourse discussion, then inspect the stan::io::var_context handling described in this issue. The work is complete when users can access the initial parameter values on the constrained scale; support for transformed parameters, generated quantities, and the unconstrained scale is lower priority.