chore: update token use in analyze dependents workflow to unblock automerges

[brian-smith-tcril]

Resolves #3383

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.91%. Comparing base (69e4fb1) to head (a7aac9a).

Additional details and impacted files

@@              Coverage Diff              @@
##           release-23.x    #3402   +/-   ##
=============================================
  Coverage         93.91%   93.91%           
=============================================
  Files               232      232           
  Lines              3943     3943           
  Branches            933      901   -32     
=============================================
  Hits               3703     3703           
  Misses              236      236           
  Partials              4        4           

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