Update docs for trace and bug fixes

[ultmaster]

This pull request adds documentation and CI support for new integrations (MCP and OpenAI), and improves test workflows to handle context files and additional integration scenarios. The main changes are grouped into documentation additions for new integrations, and enhancements to the GitHub Actions workflows for broader integration testing and context-aware execution.

Documentation for new integrations:

• Added a new guide for integrating POML with AgentOps, detailing installation, configuration, usage, and trace data examples. (docs/python/integration/agentops.md)
• Added a new guide for integrating POML with LangChain, including usage examples, feature comparisons, and template differences. (docs/python/integration/langchain.md)
• Added a new guide for working with MCP (Model Context Protocol), including a dynamic tool POML template, a full integration example, and comparison with direct MCP usage. (docs/python/integration/mcp.md)

GitHub Actions workflow enhancements:

• Extended integration test matrix to include mcp and openai in addition to existing integrations, enabling automated testing for these new integrations. (.github/workflows/test-integration.yml, .github/workflows/shared-test-integration.yml) [1] [2] [3]
• Updated the shared integration workflow to handle MCP and OpenAI: added setup steps for the MCP server and split out OpenAI-specific tests to run only when the integration is set to openai. (.github/workflows/shared-test-integration.yml) [1] [2] [3]

Test execution improvements:

• Modified example test steps to check for the presence of a .context.json file and use it if available, both for poml and poml-cli commands. (.github/workflows/test-after-publish.yml) [1] [2]

[Copilot]

Pull Request Overview

This PR updates documentation for POML trace functionality and fixes bugs related to OpenAI API format handling. The changes focus on improving POML's integration capabilities and adding comprehensive documentation for Python integrations.

• Fixes OpenAI Chat Completion API format issues in tool definitions and response format schemas
• Adds extensive documentation for Python integrations (OpenAI, LangChain, MCP, MLflow, AgentOps, Weave)
• Enhances tracing functionality with better context handling and local variable scoping

Reviewed Changes

Copilot reviewed 37 out of 46 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
python/tests/test_poml_formats.py	Fixes OpenAI format structure by adding missing wrapper objects for tools and response_format
python/tests/test_examples.py	Adds context file loading support for example tests
python/tests/integration/	Adds comprehensive integration test files for OpenAI, MCP server functionality
python/tests/assets/	Adds POML template files for testing tool calls, response formats, and dynamic tools
python/poml/api.py	Fixes OpenAI format generation to properly wrap tools and response_format schemas
packages/poml/file.tsx	Improves let variable handling with better local vs global context separation
docs/python/	Adds comprehensive integration documentation for multiple platforms
examples/	Adds math calculation example files with context support

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