Resuscitate the Cloudy example and add Documentation

[bielim]

Purpose

Closes #256

Resuscitate the Cloudy example. The example demonstrates the full CES pipeline using a simple microphysics model but is currently deprecated.
The goal is to get it working again, and to include a version with a Random Feature emulator in addition to the currently implemented Gaussian Process emulator.
Documentation will be added as well.

Docs can be found here

Content

• Get the deprecated example to work again
• Add a version using a RF emulator
• Clean-up
• Documentation

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (a621a04) 88.09% compared to head (e34b5f0) 88.07%.
Report is 4 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #253      +/-   ##
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- Coverage   88.09%   88.07%   -0.02%     
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  Files           7        7              
  Lines        1134     1124      -10     
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- Hits          999      990       -9     
+ Misses        135      134       -1     

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[odunbar]

Thanks very much for the hard work! This looks awesome! I have some small comments and a couple of larger points:

• Could you plot corner for the results- i have a snippet you can copy paste for this (rather than marginals just to emphasise that the posterior is a joint distributions)
• I think the Manifest should be removed, and the Project toml can pin a cloudy version, and can add in EKP and/or CES versions (note that EKP is also within CES so you could just import CES and do using CalibrateEmulateSample.EnsembleKalmanProcesses) for example
• the modularity for GP & RF should only be in the ML tool, the Emulator object should be constructed same for both options (and shouldn't effect the results)

[odunbar]

This looks great now thank you!

• One very small comment, could you label the figures in assets with cloudy_... just so we can distinguish them?
• Can you go to your base of your CES repo and call
  julia --project=.dev .dev/climaformat.jl to make the formatter happy, (and push the relevant changed files)

It would be good to see the vector case in here. I'd advocate for
NonSeperable(LowRankFactor(r)) for some low-ish rank r
and you can set decorrelate = false in the emulator for this case (so it doesn't use the SVD). However, if this is too much work, then I would also be happy to see this merged after the above small comments.

[odunbar]

I'm removing the .dev Manifest, and then will merge on all success

[odunbar]

Windows failure is still being resolved in #262 - it is unrelated to this PR.