Add tool approval integration for Vercel AI adapter

[bendrucker]

Adds tool approval integration for the Vercel AI adapter, enabling human-in-the-loop workflows with the AI SDK.

This PR builds on pydantic#3760 and implements the basic plumbing for tool approval. The integration is functional for emitting approval requests and parsing approval responses, but does not yet automatically wire up the full flow.

Changes

• Adds ToolApprovalRequested and ToolApprovalResponded types to represent approval state
• Adds approval field to all ToolUIPart and DynamicToolUIPart variants
• Emits ToolApprovalRequestChunk when agent returns DeferredToolRequests
• Adds deferred_tool_results property on VercelAIAdapter to extract approval responses from incoming tool parts
• Adds extract_deferred_tool_results() class method for parsing approvals

How It Works

Approval Request (server → client):

1. Agent tool has requires_approval=True
2. When model calls the tool, agent returns DeferredToolRequests
3. VercelAIEventStream.handle_run_result() emits tool-approval-request chunk
4. Client receives chunk and shows approval UI

Approval Response (client → server):

1. User approves or denies in the UI
2. Client updates the tool part's approval field with {id, approved, reason?}
3. Next SubmitMessage includes tool parts with approval responses
4. VercelAIAdapter.deferred_tool_results extracts these into DeferredToolResults

Open Questions

1. Automatic vs Manual Integration

Currently, users must manually wire up the deferred tool results:

adapter = VercelAIAdapter(agent, request)
deferred = adapter.deferred_tool_results

# User must pass deferred_tool_results to run_stream
events = adapter.run_stream(deferred_tool_results=deferred)

Question: Should run_stream() automatically use self.deferred_tool_results when not explicitly provided? This would make the integration seamless but less explicit.

2. Approval ID Tracking

We generate a UUID for approval_id in ToolApprovalRequestChunk, but the AI SDK uses this ID to track the approval lifecycle. The ToolApprovalResponded.id field should match the original approval_id.

Question: Do we need to store/track these approval IDs to validate they match on response? Currently we don't validate this.

3. ToolOutputDeniedChunk

The ToolOutputDeniedChunk type exists but isn't emitted anywhere. In Pydantic AI, denied tool results flow as regular ToolReturnPart with the denial message as content.

Question: Should we emit ToolOutputDeniedChunk when the deferred tool result is a ToolDenied? This would require tracking which tool calls were denied through the agent run.

4. Message History Handling

When continuing with deferred tool results, the message history needs to include the original messages. Currently the adapter's messages property processes all incoming messages, but:

Question: Should tool parts with pending approvals (only ToolApprovalRequested, not ToolApprovalResponded) be filtered out or handled specially when building message history?

Testing

• Added test for ToolApprovalRequestChunk emission when requires_approval=True tool is called
• Added tests for extract_deferred_tool_results() covering approved, denied, and no-approval cases

References

• Depends on: Add AI SDK data chunk ID and tool approval types pydantic/pydantic-ai#3760
• AI SDK tool approval docs: https://ai-sdk.dev/docs/ai-sdk-ui/chatbot-with-tool-usage#human-in-the-loop
• Pydantic AI deferred tools: https://ai.pydantic.dev/deferred-tools/