Chore: use shutdown result type in LogExporter trait

[scottgerring]

Fixes #
Design discussion issue (if applicable) #

Changes

Please provide a brief description of the changes here.

Merge requirement checklist

• CONTRIBUTING guidelines followed
• Unit tests added/updated (if applicable)
• Appropriate CHANGELOG.md files updated for non-trivial, user-facing changes
• Changes in public API reviewed (if applicable)

[cijothomas]

this should be ShutdownError::InternalFailure?
Same with the else branch here dealing with mutexpoison.

[scottgerring]

@cijothomas to be clear you're suggesting that we change trait LogProcessor's shutdown signature as well, right?

[cijothomas]

yes

[codecov]

Codecov Report

Attention: Patch coverage is 46.42857% with 15 lines in your changes missing coverage. Please review.

Project coverage is 79.5%. Comparing base (dde68a0) to head (106e4b4).

Files with missing lines	Patch %	Lines
opentelemetry-otlp/src/exporter/http/logs.rs	0.0%	6 Missing ⚠️
opentelemetry-sdk/src/logs/export.rs	0.0%	3 Missing ⚠️
opentelemetry-otlp/src/exporter/tonic/logs.rs	0.0%	2 Missing ⚠️
...y-sdk/src/logs/log_processor_with_async_runtime.rs	71.4%	2 Missing ⚠️
opentelemetry-stdout/src/logs/exporter.rs	0.0%	2 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #2588     +/-   ##
=======================================
- Coverage   79.5%   79.5%   -0.1%     
=======================================
  Files        118     118             
  Lines      22480   22498     +18     
=======================================
+ Hits       17878   17886      +8     
- Misses      4602    4612     +10     

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