Add experimental Pigeons sampling and evidence estimation

[BJMCox]

Add experimental PigeonsSampling for posterior sampling and evidence estimation with fixed-reference, variational, and stabilized parallel tempering. Support BAT initialization, Pigeons explorers, and multithreading. Restore sample shapes and densities, and return one final-round target trace with autocorrelation ESS.

Expose adapted temperature ladders, swap probabilities, barriers, and round-trip diagnostics. Preserve prior mass when estimating evidence and keep variational configurations reusable. Round-trip counters return missing for unequal stabilized legs because Pigeons currently counts them incorrectly.

Validation: all 29 optional assertions pass on Julia 1.13.0 with Pigeons 0.4.11. Coverage includes weighted evidence across reference fitting, initialization, shape restoration, threaded replay, variational reuse, multimodality, and AutoMALA. Both documentation examples pass. Separate probes confirm unchanged default RNG replay and stable evidence at large log weights. Tests remain in the separate optional Pigeons CI job.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 68.62%. Comparing base (1995c02) to head (eeac0c9).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #580      +/-   ##
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+ Coverage   66.89%   68.62%   +1.72%     
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  Files         121      122       +1     
  Lines        7087     7183      +96     
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+ Hits         4741     4929     +188     
+ Misses       2346     2254      -92     

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