Logs SDK - use OTelSdkError, OTelSdkResult

[lalitb]

TBD - changelog

Completes the initial work done by @scottgerring in #2588. Thanks @scottgerring.

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)

[codecov]

Codecov Report

Attention: Patch coverage is 49.66887% with 76 lines in your changes missing coverage. Please review.

Project coverage is 79.0%. Comparing base (69e7e89) to head (b568d04).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
opentelemetry-otlp/src/exporter/http/logs.rs	0.0%	23 Missing ⚠️
opentelemetry-sdk/src/logs/log_processor.rs	51.5%	16 Missing ⚠️
opentelemetry-sdk/src/logs/logger_provider.rs	60.6%	13 Missing ⚠️
opentelemetry-otlp/src/exporter/tonic/logs.rs	0.0%	8 Missing ⚠️
...y-sdk/src/logs/log_processor_with_async_runtime.rs	77.7%	4 Missing ⚠️
opentelemetry-stdout/src/logs/exporter.rs	0.0%	4 Missing ⚠️
opentelemetry-sdk/src/logs/export.rs	0.0%	3 Missing ⚠️
opentelemetry-sdk/src/logs/in_memory_exporter.rs	85.7%	2 Missing ⚠️
opentelemetry-appender-tracing/src/layer.rs	83.3%	1 Missing ⚠️
opentelemetry-otlp/src/logs.rs	0.0%	1 Missing ⚠️
... and 1 more

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #2625     +/-   ##
=======================================
- Coverage   79.1%   79.0%   -0.1%     
=======================================
  Files        119     119             
  Lines      22555   22579     +24     
=======================================
+ Hits       17842   17851      +9     
- Misses      4713    4728     +15     

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[cijothomas]

Awesome!
Thanks @lalitb and @scottgerring

[scottgerring]

Perfect! Thanks for finishing this off @lalitb 🥳