fix: add context timeout to health check

[gaius-qi]

Description

Related Issue

Fixes #2930

Motivation and Context

Screenshots (if appropriate)

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation Update (if none of the other choices apply)

Checklist

• My change requires a change to the documentation.
• I have updated the documentation accordingly.
• I have read the CONTRIBUTING document.
• I have added tests to cover my changes.

[codecov]

Codecov Report

Merging #2943 (0165fdf) into main (839e476) will not change coverage.
The diff coverage is n/a.

❗ Current head 0165fdf differs from pull request most recent head 89323da. Consider uploading reports for the commit 89323da to get more accurate results

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2943   +/-   ##
=======================================
  Coverage   51.08%   51.08%           
=======================================
  Files         161      161           
  Lines       21831    21831           
=======================================
  Hits        11152    11152           
  Misses      10019    10019           
  Partials      660      660           

Flag	Coverage Δ
Object-compatibility-e2etests	?
e2etests	?
unittests	51.08% <ø> (ø)

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