Fix the CM statistics async publish placement (backport #2865)

[mergify]

Right now, the image looks like below instead of the expected_total_time. inorder to fix it, we need to move the statistics publishing to the write callback part, and the other one is good at its place

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This is an automatic backport of pull request #2865 done by [Mergify](https://mergify.com).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 89.44%. Comparing base (812f8cd) to head (0d21fd6).
⚠️ Report is 1 commits behind head on jazzy.

Additional details and impacted files

@@            Coverage Diff             @@
##            jazzy    #2868      +/-   ##
==========================================
- Coverage   89.44%   89.44%   -0.01%     
==========================================
  Files         155      155              
  Lines       18021    18021              
  Branches     1465     1465              
==========================================
- Hits        16119    16118       -1     
  Misses       1329     1329              
- Partials      573      574       +1     

Flag	Coverage Δ
unittests	89.44% <ø> (-0.01%)	⬇️

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Files with missing lines	Coverage Δ
controller_manager/src/controller_manager.cpp	77.17% <ø> (-0.05%)	⬇️

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