[WIP] Update to Distributions 0.24.12

[devmotion]

This PR updates DistributionsAD to Distributions >= 0.24.12. The latest version of Distributions contains many things that previously had to be fixed in DistributionsAD and therefore allows us to remove a large part of DistributionsAD. E.g., it supports automatically

• Dirichlet distributons with general parameter vectors (Allow general vectors in Dirichlet [BREAKING] JuliaStats/Distributions.jl#1243)
• logpdf for matrices and arrays of samples (No pre-allocation of outputs for logpdf and pdf JuliaStats/Distributions.jl#1263)
• construction of more general DiscreteNonParametric distributions (Fix conversion error with DiscreteNonParametric JuliaStats/Distributions.jl#1184)
• a faster more accurate pdf of the Poisson binomial distribution that does not use FFTs (Faster, more accurate Poisson Binomial PMF JuliaStats/Distributions.jl#1198)

This allows us e.g. to remove the overly optimistic logpdf pullbacks and fixes #121 since Distributions now contains the fix suggested in #121 (comment).

[devmotion]

Seems that eltype(::Type{<:TrackedArray}) isa TrackedReal causes problems with Dirichlet and the Dirichlet tests for ReverseDiff yield the same errors as in #146. Might be better to remove the Dirichlet changes from this PR.

[devmotion]

The ReverseDiff adjoints for simplex_logpdf are wrong, but it seems that they are not responsible for the ReverseDiff test failures.

[yebai]

Thanks, @devmotion - it looks good to me!

[yebai]

Ps, it seems the test for ReverseDiff is broken: https://github.com/TuringLang/DistributionsAD.jl/pull/150/checks?check_run_id=1783614538#step:5:231

[devmotion]

I assume the test failures are (at least partly) fixed by #151.

[yebai]

@devmotion Just a gentle reminder - happy to merge this once the merge conflicts are resolved and CI passing.

[devmotion]

I'll close this since it is partly covered by #198 and it is probably cleaner to make a new PR for the remaining changes in this PR.