Logging improvements

[gavin-aguiar]

Description

Added a few logging improvements which should improve cold starts.

Fixes #

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PR information

• The title of the PR is clear and informative.
• There are a small number of commits, each of which has an informative message. This means that previously merged commits do not appear in the history of the PR. For information on cleaning up the commits in your pull request, see this page.
• If applicable, the PR references the bug/issue that it fixes in the description.
• New Unit tests were added for the changes made and CI is passing.

Quality of Code and Contribution Guidelines

• I have read the contribution guidelines.

[codecov]

Codecov Report

Merging #1228 (be9caae) into dev (4a9a38e) will decrease coverage by 51.99%.
The diff coverage is 0.00%.

❗ Current head be9caae differs from pull request most recent head 78dc021. Consider uploading reports for the commit 78dc021 to get more accurate results

@@             Coverage Diff             @@
##              dev    #1228       +/-   ##
===========================================
- Coverage   83.97%   31.98%   -51.99%     
===========================================
  Files          34       34               
  Lines        1903     1904        +1     
  Branches      366      365        -1     
===========================================
- Hits         1598      609      -989     
- Misses        234     1294     +1060     
+ Partials       71        1       -70     

Flag	Coverage Δ
unittests	31.98% <0.00%> (-51.94%)	⬇️

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

Impacted Files	Coverage Δ
azure_functions_worker/dispatcher.py	19.39% <0.00%> (-69.75%)	⬇️
azure_functions_worker/utils/dependency.py	33.08% <0.00%> (-53.39%)	⬇️

... and 22 files with indirect coverage changes