Add integration guides for OpenAI, Anthropic, LangChain, FastAPI, and streaming

[amavashev]

Summary

This PR adds comprehensive how-to guides for integrating the Cycles budget management system with popular Python frameworks and LLM providers. These guides provide practical patterns for cost-controlling API calls across different use cases.

Changes

• OpenAI Integration Guide (how-to/integrating-cycles-with-openai.md): Demonstrates the @cycles decorator pattern for guarding chat completions with budget reservations, cost estimation strategies, budget exhaustion handling, and metrics reporting.

• Anthropic Integration Guide (how-to/integrating-cycles-with-anthropic.md): Shows both decorator-based simple calls and programmatic per-turn budget tracking for agentic workflows with tool use, including pricing reference table.

• LangChain Integration Guide (how-to/integrating-cycles-with-langchain.md): Explains the callback handler approach (CyclesBudgetHandler) for wrapping every LLM call in LangChain applications, with examples for chat models and agents with tools.

• FastAPI Integration Guide (how-to/integrating-cycles-with-fastapi.md): Covers client lifecycle management, exception handlers for budget errors, preflight middleware with decide(), per-tenant isolation, and budget dashboard endpoints.

• Streaming Responses Guide (how-to/handling-streaming-responses-with-cycles.md): Addresses the reserve → stream → commit pattern for streaming LLM responses, TTL considerations, release-on-failure semantics, and cap respecting.

• Documentation Navigation: Updated .vitepress/config.ts to include the new guides in the sidebar navigation under the how-to section.

Notable Implementation Details

• Each guide includes runnable code examples with proper error handling and idempotency key management
• Pricing tables and token cost calculations are provided for reference
• Guides emphasize the distinction between decorator-based (simple, automatic) and programmatic (complex, manual) approaches
• TTL and cap-respecting patterns are consistently demonstrated across all integrations
• Links to full example scripts in the repository are included for each guide

https://claude.ai/code/session_019RuDwakEwtZDbEMYNvesUF