[WilliamK112]

Summary

• prevent be, n_jobs, and verbose from colliding with arguments already controlled by silhouette_score and silhouette_samples
• handle be consistently whether it arrives through metric_params or direct keyword input
• document which metric parameters are overridden or inferred
• add regression coverage for both public functions and both input paths

The precomputed-metric behavior discussed in #714 is intentionally unchanged.

Closes #713

Validation

• pytest tests/test_clustering.py -q — 13 passed
• pytest --doctest-modules tslearn/clustering/utils.py -q — 3 passed
• pytest -q --doctest-modules — 1,168 passed, 44 skipped, 11 xfailed
• git diff --check

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.26%. Comparing base (a4eb51a) to head (0b5fbd1).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #718      +/-   ##
==========================================
+ Coverage   95.21%   95.26%   +0.04%     
==========================================
  Files          83       83              
  Lines        7902     7916      +14     
==========================================
+ Hits         7524     7541      +17     
+ Misses        378      375       -3     

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[charavelg]

Thanks for the fix!!!