Fix async_monkey_patch typo and update context API usage

[Gundue]

• Corrected typo in async_monkey_patch_for_pinpoint (was 'asyn_monkey_patch_for_pinpoint')
• Removed use_starlette_context, updated to use_thread_local_context and use_asyncio_local_context
• Ensures compatibility with latest pinpoint agent and async context handling

Describe your changes

why we need this pr?

Issue ticket number and link

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Checklist before requesting a review

• I have performed a self-review of my code
• If it is a core feature, I have added thorough tests.
• Do we need to implement analytics?
• Will this be part of a product update? If yes, please write one phrase about this update.

[eeliu]

Thanks

[eeliu]

LGTM

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.57%. Comparing base (5187cc0) to head (c14c69a).
⚠️ Report is 70 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #731      +/-   ##
==========================================
- Coverage   80.79%   80.57%   -0.23%     
==========================================
  Files          22       22              
  Lines        1536     1539       +3     
  Branches      165      168       +3     
==========================================
- Hits         1241     1240       -1     
- Misses        162      165       +3     
- Partials      133      134       +1     

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