[Backport maintenance/3.3.x] Improve backport job permissions

[cdce8p]

Backport fe5bb6c from #2749.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

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Additional details and impacted files

@@                 Coverage Diff                  @@
##             maintenance/3.3.x    #2750   +/-   ##
====================================================
  Coverage                     ?   93.06%           
====================================================
  Files                        ?       93           
  Lines                        ?    11082           
  Branches                     ?        0           
====================================================
  Hits                         ?    10313           
  Misses                       ?      769           
  Partials                     ?        0           

Flag	Coverage Δ
linux	92.92% <ø> (?)
pypy	93.06% <ø> (?)
windows	93.04% <ø> (?)

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