Add AI SDK data chunk ID and tool approval types

[bendrucker]

Adds missing fields to Vercel AI adapter types for full AI SDK compatibility, addressing data part reconciliation and other protocol gaps.

Changes

• DataChunk: Adds optional id field for data part reconciliation and transient field for non-persistent data
• FinishChunk: Adds finish_reason field with standard stop reasons (stop, length, content-filter, tool-calls, error, other, unknown)
  • Populated from ModelResponse.finish_reason in handle_run_result
  • Set to error in on_error handler
• Adds ToolApprovalRequestChunk and ToolOutputDeniedChunk types for human-in-the-loop tool approval workflows

Future Work

Tool approval integration will be addressed in a separate PR. This requires:

1. Emitting ToolApprovalRequestChunk when agent output is DeferredToolRequests
2. Exploring how Vercel AI SDK sends back approval/denial responses to map them to DeferredToolResults
3. Handling ToolOutputDeniedChunk — currently Pydantic AI doesn't distinguish denied tool results from normal results at the event stream level (denied results flow as FunctionToolResultEvent with ToolReturnPart)

Testing

• Added test for DataChunk with id field to verify reconciliation IDs serialize correctly in the SSE stream
• Added test for DataChunk with transient: true to verify non-persistent data chunks are encoded properly
• Updated existing error handling tests to verify finishReason: 'error' is set correctly

[DouweM]

Do we ever receive (the part version) of this, and should we handle it? We'll likely need it for https://ai.pydantic.dev/deferred-tools/#human-in-the-loop-tool-approval

[bendrucker]

Forgot to post this comment, splitting off deferred tool <> approval integration definitely makes sense based on my epxloration. I will slim this down to types + finish reason and then kick off a draft for tool approval logic.

Dug into denials a bit, approvals are closer to being easily supported.

When a user denies a tool execution, Pydantic AI doesn't have a distinct event type for it. Denied tool results flow as regular FunctionToolResultEvent with ToolReturnPart, with the denial message as the content field. There's no way to distinguish a denial from a normal tool result at the event stream level.

So we'd need something like:

• A new event type like DeniedToolResultEvent
• A ToolDeniedPart message type (vs ToolReturnPart)

[DouweM]

When a user denies a tool execution, Pydantic AI doesn't have a distinct event type for it.

@bendrucker Hmm, Pydantic AI doesn't have an event for denials because denials never originate in Pydantic AI itself, they come from the user in the form of DeferredToolResults passed into agent.run, so I'm not sure why Vercel AI expects us to yield denial chunks to them, rather than them sending approval/denial parts or metadata to us?

[bendrucker]

Yeah you're right, I need to keep reading. The only thing I can think of is that the client is expecting an acknowledgement from the server of the denial. I've opened #3772 with half-working code and some notes for discussion. Really an issue with illustrative code attached right now, not close to reviewable/mergeable. If you want to dig further/comment, I'm certainly interested, but otherwise will spend some more time validating the client-side behavior and getting the PR to a reviewable state.