[e2e] Enable back end to end test on background tasks (#7378)

[aHenryJard]

Proposed changes

• Background task was disabled because too flaky, it seems more stable now with CI improvement and maybe some code fix too.

Related issues

• relates to end to end effort #7378

Checklist

• [ ] I consider the submitted work as finished
• [ ] I tested the code for its functionality
• [ ] I wrote test cases for the relevant uses case (coverage and e2e)
• [ ] I added/update the relevant documentation (either on github or on notion)
• [ ] Where necessary I refactored code to improve the overall quality

Further comments

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 66.06%. Comparing base (a032eb7) to head (045c6da). Report is 6 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #8187   +/-   ##
=======================================
  Coverage   66.06%   66.06%           
=======================================
  Files         597      597           
  Lines       59732    59732           
  Branches     6080     6083    +3     
=======================================
+ Hits        39460    39462    +2     
+ Misses      20272    20270    -2     

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[aHenryJard]

Run number 1: all green in Drone, restarting build for both pr and push.

[aHenryJard]

Run number 2: all green

[aHenryJard]

Run number 3 after rebase: all green, let's open for review.