[Backport 3.1] Refine cold-start, window delay, and task updates

[opensearch-trigger-bot]

Backport 08dceb4 from #1496.

[codecov]

Codecov Report

Attention: Patch coverage is 30.76923% with 9 lines in your changes missing coverage. Please review.

Project coverage is 81.41%. Comparing base (ed4658d) to head (936df0d).
Report is 1 commits behind head on 3.1.

Files with missing lines	Patch %	Lines
...ansport/BaseSuggestConfigParamTransportAction.java	0.00%	5 Missing ⚠️
.../opensearch/forecast/ml/ForecastCheckpointDao.java	0.00%	2 Missing ⚠️
...a/org/opensearch/timeseries/ml/ModelColdStart.java	33.33%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff            @@
##                3.1    #1497   +/-   ##
=========================================
  Coverage     81.40%   81.41%           
- Complexity     5972     5976    +4     
=========================================
  Files           536      536           
  Lines         24205    24214    +9     
  Branches       2443     2446    +3     
=========================================
+ Hits          19705    19714    +9     
- Misses         3291     3293    +2     
+ Partials       1209     1207    -2     

Flag	Coverage Δ
plugin	81.41% <30.76%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...rc/main/java/org/opensearch/ad/ml/ADColdStart.java	80.85% <100.00%> (+0.20%)	⬆️
...va/org/opensearch/timeseries/task/TaskManager.java	80.69% <100.00%> (-0.58%)	⬇️
.../opensearch/forecast/ml/ForecastCheckpointDao.java	22.43% <0.00%> (-0.15%)	⬇️
...a/org/opensearch/timeseries/ml/ModelColdStart.java	78.32% <33.33%> (-0.78%)	⬇️
...ansport/BaseSuggestConfigParamTransportAction.java	51.48% <0.00%> (-2.13%)	⬇️

... and 9 files with indirect coverage changes

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