[Volkan Cetin (vlkncetin)]

Backports #8935 to release-14.0.

• Parallelizes source connections and connectivity probes across source nodes.
• Preserves result ordering and true/false/NULL semantics.
• Includes the cancellation-test synchronization correction from the release-13.2 backport (Backport #8935: Parallelize cluster node health checks (release-13.2) #8938).

Production code matches #8935; both changed files match #8938.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 88.56%. Comparing base (22b5d0b) to head (717f783).

Additional details and impacted files

@@                   Coverage Diff                    @@
##           bp-8766-release-14.0    #8939      +/-   ##
========================================================
+ Coverage                 88.25%   88.56%   +0.31%     
========================================================
  Files                       291      291              
  Lines                     65155    65194      +39     
  Branches                   8215     8219       +4     
========================================================
+ Hits                      57503    57740     +237     
+ Misses                     5212     5083     -129     
+ Partials                   2440     2371      -69     

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