Ensure AG-UI state is isolated between requests.

[DouweM]

Fixes #2339

[hyperlint-ai]

PR Change Summary

Isolated AG-UI state management between requests to enhance reliability and validation.

• Updated documentation to clarify the use of custom dependencies for AG-UI state management.
• Introduced a requirement for custom dependencies to implement the StateHandler protocol for state isolation.
• Enhanced validation process for AG-UI state using Pydantic BaseModel.

Modified Files

• docs/ag-ui.md

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