Fix threading issue for logging

[cheng-tan]

Why are these changes needed?

• Fix mypy errors for logging feature
• Fix threading error for logging feature

Related issue number

closes #1822

Checks

• I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://microsoft.github.io/autogen/docs/Contribute#documentation to build and test documentation locally.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 68.81720% with 29 lines in your changes are missing coverage. Please review.

Project coverage is 47.62%. Comparing base (2a62ffc) to head (58b7b53).

Files	Patch %	Lines
autogen/runtime_logging.py	43.33%	12 Missing and 5 partials ⚠️
autogen/logger/sqlite_logger.py	77.77%	12 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1901       +/-   ##
===========================================
+ Coverage   37.21%   47.62%   +10.41%     
===========================================
  Files          64       64               
  Lines        6815     6834       +19     
  Branches     1496     1629      +133     
===========================================
+ Hits         2536     3255      +719     
+ Misses       4067     3310      -757     
- Partials      212      269       +57     

Flag	Coverage Δ
unittests	47.49% <68.81%> (+10.28%)	⬆️

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