add build and push workflow to run integration test branch

[Basma1912]

One-line summary

• I used an AI to write some of this code.

Significant changes and points to review

Issue / Bugzilla link

Testing

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 78.64%. Comparing base (1428aa5) to head (f55741f).
Report is 290 commits behind head on run-integration-tests.

Additional details and impacted files

@@                    Coverage Diff                    @@
##           run-integration-tests   #15439      +/-   ##
=========================================================
+ Coverage                  77.18%   78.64%   +1.46%     
=========================================================
  Files                        159      155       -4     
  Lines                       8239     8157      -82     
=========================================================
+ Hits                        6359     6415      +56     
+ Misses                      1880     1742     -138     

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