fix: Only log error that originally caused the crash

[FrederikBolding]

The crash logging that we recently added would trigger for any unhandled error, including cancelled requests during a crash. This PR only logs the original crash error.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.28%. Comparing base (235feed) to head (ba97ff5).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #3569   +/-   ##
=======================================
  Coverage   98.28%   98.28%           
=======================================
  Files         417      417           
  Lines       11769    11771    +2     
  Branches     1830     1832    +2     
=======================================
+ Hits        11567    11569    +2     
  Misses        202      202           

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