chore: Modernize server-ai package and provider READMEs to current SDK

[jsonbailey]

Summary

• Modernize three READMEs (packages/sdk/server-ai/README.md, packages/ai-providers/server-ai-openai/README.md, packages/ai-providers/server-ai-langchain/README.md) to current Python AI SDK 0.19+ APIs
• Replace nonexistent from ldai import init / init(ld_client) (in both provider READMEs) with from ldai import LDAIClient / LDAIClient(ld_client)
• Update server-ai README managed-model example: model.invoke() → model.run(); .message.content → .content (ManagedResult is flat); remove nonexistent model.get_messages() (replace with model.get_config().messages)
• Replace nonexistent LangChainProvider class throughout server-ai README with current create_langchain_model and bare get_ai_metrics_from_response helper
• Swap track_metrics_of / track_metrics_of_async arg order to (extractor, callable) per 0.19 signature
• Canonicalize imports: from ldai.providers.types → from ldai.providers (LDAIMetrics) + from ldai.tracker (TokenUsage)
• Align LangChain README's manual-runner example to import LangChainModelRunner (which it actually instantiates)

Refs AIC-2383. This PR is part of the AI Configs docs/example modernization sweep tracked in `python-agent-work/all-docs-review.md`.

Test plan

• Grep sweep confirms zero remaining `from ldai import init`, `LangChainProvider`, `model.invoke(`, `.message.content`, `model.get_messages`, `track_metrics_of(lambda:` in the 3 modified files
• Each Python snippet in the READMEs is syntactically valid (manual paste-into-REPL or `python -m py_compile` via a temp file)
• At least one provider snippet runs end-to-end against current SDK to confirm no runtime errors

🤖 Generated with Claude Code

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Note

Low Risk
Documentation-only changes that update example code to match current SDK APIs; low risk aside from potentially breaking copy/paste snippets if any call signatures were misunderstood.

Overview
Modernizes the Python AI SDK and provider READMEs to current APIs by switching initialization to LDAIClient(ld_client) and updating ManagedModel examples to use model.run() and the flattened result.content.

Refreshes provider-centric examples to remove outdated LangChainProvider references in favor of create_langchain_model/get_ai_metrics_from_response, fixes tracking helper call signatures (track_metrics_of/track_metrics_of_async), and updates imports/types (LDAIMetrics, TokenUsage) and the LangChain manual-runner example to use LangChainModelRunner.

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