feat(core): move to OTEL backbone

[hassiebp]

Greptile Summary

Disclaimer: Experimental PR review

This PR implements a major architectural change by migrating the Langfuse Python SDK to use OpenTelemetry (OTel) as its backbone for tracing and observability. However, the PR completely removes several critical example applications without proper migration paths.

• Removes entire Django and FastAPI example applications including configuration, routes and documentation without providing replacements or migration guides
• Introduces comprehensive OTel-based tracing with proper span handling, sampling, and distributed context management in _client/ directory
• Replaces custom task management and ingestion with OTel's infrastructure for better standardization and interoperability
• Improves thread safety and error handling through OTel's context management and span processors
• Critical: Example applications should be preserved or migrated rather than removed to maintain SDK usability

[ellipsis-dev]

⚠️ This PR is too big for Ellipsis, but support for larger PRs is coming soon. If you want us to prioritize this feature, let us know at help@ellipsis.dev

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[greptile-apps]

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