Use vercelRunOutcome in Vercel AI SDK Core framework guide

The agent route snippets piped the stream and called run.end({ reason })
directly, skipping vercelRunOutcome. This diverged from the getting started
guide and the 0.2.0 blog post, and dropped tool-call suspension and the
finishReason rejection guard. Align both snippets and the explanation with
the canonical pattern.

Fixes AIT-1034

Author: rainbowFi

src/pages/docs/ai-transport/frameworks/vercel-ai-sdk-core.mdx

@@ -46,8 +46,10 @@ On the server, AI Transport replaces `createUIMessageStreamResponse()` with `Run
 return createUIMessageStreamResponse({ stream: result.toUIMessageStream() });
 
 // After: Ably transport
-const { reason } = await run.pipe(result.toUIMessageStream());
-await run.end({ reason });
+const pipeResult = await run.pipe(result.toUIMessageStream());
+const outcome = await vercelRunOutcome(pipeResult, result.finishReason);
+await run.end(outcome);
+
 return Response.json({ invocationId: run.invocationId });
 ```
 </Code>
@@ -59,9 +61,9 @@ A full agent route:
 import { after } from 'next/server';
 import { streamText, convertToModelMessages } from 'ai';
 import { anthropic } from '@ai-sdk/anthropic';
-import Ably from 'ably';
+import * as Ably from 'ably';
 import { Invocation } from '@ably/ai-transport';
-import { createAgentSession } from '@ably/ai-transport/vercel';
+import { createAgentSession, vercelRunOutcome } from '@ably/ai-transport/vercel';
 
 const ably = new Ably.Realtime({ key: process.env.ABLY_API_KEY });
 
@@ -81,12 +83,17 @@ export async function POST(req) {
       abortSignal: run.abortSignal,
     });
 
-    const { reason } = await run.pipe(result.toUIMessageStream());
-    await run.end({ reason });
+    const pipeResult = await run.pipe(result.toUIMessageStream());
+    const outcome = await vercelRunOutcome(pipeResult, result.finishReason);
+    if (outcome.reason === 'suspend') {
+      await run.suspend();
+    } else {
+      await run.end(outcome);
+    }
     session.close();
   });
 
-  return Response.json({ invocationId: run.invocationId });
+  return Response.json({ runId: run.runId, invocationId: run.invocationId });
 }
 ```
 </Code>
@@ -95,7 +102,7 @@ The integration has three pieces:
 
 1. The `UIMessageCodec` encodes Vercel's `UIMessageChunk` events as Ably messages. Every chunk type maps to an Ably operation with headers that track the metadata. The codec encodes on the agent and decodes on the client.
 2. `createAgentSession({ client, channelName })` from `@ably/ai-transport/vercel` constructs the agent session bound to the channel from the invocation. The default codec is `UIMessageCodec`.
-3. `run.pipe()` reads the model's `UIMessageChunk` stream, encodes each chunk, and publishes the resulting Ably messages. `run.abortSignal` wires cancellation through from the client.
+3. `run.pipe()` reads the model's `UIMessageChunk` stream, encodes each chunk, and publishes the resulting Ably messages. `run.abortSignal` wires cancellation through from the client. [`vercelRunOutcome()`](/docs/ai-transport/api/javascript/vercel/run-outcome) then maps the pipe result and Vercel's `finishReason` to the right lifecycle action: suspend the Run when the model requested tools the SDK did not auto-execute, otherwise end it with the matching reason.
 
 ## Scope and trade-offs <a id="scope"/>