Drop need for rstan in tests using posterior

[seabbs]

rstan is currently required for testing convergence but we can remove this dependency if we instead use the functionality from the posteriors package.

[athowes]

Agree on this but unsure posterior provides functionality for divergent transitions and treedepth:

[seabbs]

I think you should be able to pull what you need from the cmdstan object? https://github.com/epinowcast/epinowcast/blob/d957b21af07c7708d8ae28fc248fffe39d453828/R/model-tools.R#L277

[athowes]

I found a way to do it with brms. (Which we already depend on.)

[athowes]

I found that running using brms it saves to stanfit so you can't access the cmdstanr class functions.

I also have been finding it hard to do it with brms directly (I got the maximum treedepth but not the number of times it has been hit).