Disable Mooncake on prerelease; bump min Julia to 1.10.2; regroup CI tests

[penelopeysm]

Closes #2570

Mooncake doesn't precompile on 1.12, so this is a very similar fix to TuringLang/DynamicPPL.jl#921. I was getting tired of CI not passing, and also the whole env not precompiling meant that potential real issues would be masked.

In the process, we discovered that sample() was taking a very long time to compile on v1.10.0. This PR therefore also bumps the minimum version to 1.10.2, which is the first patch where this performance bug is fixed. See #2570 for more discussion (and #2571 where I was bisecting Julia patch versions).

I also edited CI to balance out the test times. The new groups are:

• mcmc/gibbs: ~ 45 minutes
• mcmc/Inference: ~10 minutes
• ad: ~30 minutes
• everything else: ~ 30 minutes

[github-actions]

Turing.jl documentation for PR #2569 is available at:
https://TuringLang.github.io/Turing.jl/previews/PR2569/

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 85.86%. Comparing base (1a70627) to head (30706a8).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2569   +/-   ##
=======================================
  Coverage   85.86%   85.86%           
=======================================
  Files          21       21           
  Lines        1429     1429           
=======================================
  Hits         1227     1227           
  Misses        202      202           

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[coveralls]

Pull Request Test Coverage Report for Build 15346521153

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 85.924%

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Totals
Change from base Build 15328534629:	0.0%
Covered Lines:	1227
Relevant Lines:	1428

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💛 - Coveralls

[mhauru]

Looks good. I have a slight preference for keeping more than 3 groups for quicker feedback.

[penelopeysm]

Regarding test grouping, stdlib/distributions has dropped to only 5 minutes, so I lumped it into "everything else". The rest is the same.

Between #2564 and this PR, we've gone from 6 test groups and 2.5 hours to 4 test groups and 45 minutes 😄