Test: Add enzyme and mooncake to benchmark

[seabbs]

This PR adds Enzyme.jl and Mooncake.jl to out benchmarking to see what happens. Potentially these should be split into two PRs and then kept updated as new versions of the autodiff backends are produced.

[github-actions]

Try this Pull Request!

Open Julia and type:

import Pkg
Pkg.activate(temp=true)
Pkg.add(url="https://github.com/CDCgov/Rt-without-renewal", rev="add-enzyme-mooncake", subdir="EpiAware")
using EpiAware

[seabbs]

Potentially there is a setup issue as from what I can see both fail for all benchmarks

[seabbs]

I have also inserted Enzyme and Mooncake into one of the case studies each as another small test

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.54%. Comparing base (8dc444f) to head (38e7518).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #540   +/-   ##
=======================================
  Coverage   90.54%   90.54%           
=======================================
  Files          57       57           
  Lines         825      825           
=======================================
  Hits          747      747           
  Misses         78       78           

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[seabbs]

Ha nothing is loaded - I am clearly doing a great job