[AUTO-BACKPORT release-0.38.0] 10206: ci: remove datadog from ci

[github-actions]

Backport 25179d0 from #10206.

[cla-bot]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 53.87%. Comparing base (332cefc) to head (c9e488a).
Report is 2 commits behind head on release-0.38.0.

Additional details and impacted files

@@               Coverage Diff               @@
##           release-0.38.0   #10214   +/-   ##
===============================================
  Coverage           53.87%   53.87%           
===============================================
  Files                1257     1257           
  Lines              156489   156489           
  Branches             3641     3642    +1     
===============================================
  Hits                84313    84313           
  Misses              72043    72043           
  Partials              133      133           

Flag	Coverage Δ
backend	46.07% <ø> (ø)
harness	67.37% <ø> (ø)
web	54.73% <ø> (ø)

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