Add convenience functions to handle AG-UI requests with request-specific deps

[DouweM]

Fixes #2377

[hyperlint-ai]

PR Change Summary

Enhanced AG-UI documentation by adding new convenience functions for handling requests and clarifying usage instructions.

• Introduced three new methods for running Pydantic AI agents with AG-UI: run_ag_ui(), handle_ag_ui_request(), and Agent.to_ag_ui().
• Updated the installation instructions to clarify dependencies for AG-UI integration.
• Revised the usage section to provide detailed examples for each method of running an agent.

Modified Files

• docs/ag-ui.md

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[stevenh]

Looks like this will make it a lot more flexible, similar to the original design.

Just a few questions

[stevenh]

question: should this be limited to OutputDataT to ensure the agent and output_type are compatible?

More below too.

[DouweM]

We were not actually using the OutputTypeT anywhere else (like it's used on the return value in the real agent.iter) so I think listing it here was a no-op

[stevenh]

Does it still act to enforce good calling convention still?

[DouweM]

I'm not sure exactly sure what you're getting at :) My understanding is that using a type var here is only meaningful if it's referenced in another generic param as well, either in another argument that it needs to match, or in the return type. But as we're using neither, including it would make no difference, and the method would still accept any Agent.

Note that in the output_type arg below, the iter signature this is based on uses RunOutputT in the arg (and in the return type) exactly because it could be different than the one bound to the agent at creation time.

So not sure what calling convention you're thinking of?