Sync post release workflow a bit more with other Java repos

[trask]

No description provided.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 90.18%. Comparing base (3a92740) to head (552579d).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##               main    #7755   +/-   ##
=========================================
  Coverage     90.18%   90.18%           
  Complexity     7196     7196           
=========================================
  Files           814      814           
  Lines         21722    21722           
  Branches       2125     2125           
=========================================
  Hits          19590    19590           
  Misses         1465     1465           
  Partials        667      667           

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