docs(ai-chat): guide for migrating an AI SDK route handler to chat.agent (#4519)

## Summary

Adds a docs page for developers who already have a working Vercel AI SDK
chat app (`useChat` on the client, an `app/api/chat/route.ts` calling
`streamText`) and want to move it to `chat.agent`. There was no page
covering that path. `ai-chat/upgrade-guide` reads like it should be the
one, but it covers moving prerelease `chat.agent` code to the Sessions
release, which is a different reader.

The page is structured around what stays, what goes, and what is new,
because the reassuring part of this migration is how much is untouched:
the `streamText` call, model config, tool definitions, `useChat`, and
all message rendering carry over as-is. What gets deleted is the route
handler, the persistence glue wired into it, and any resumable-stream
setup. What is new is the agent task, two server actions, and
`useTriggerChatTransport`.

Covers moving tools onto the agent config so `toModelOutput` survives
past turn one, where existing database persistence goes
(`hydrateMessages` plus the turn hooks), a short section on what
durability you get once you are across, a note that
Hono/SvelteKit/Express follow the same shape, and a gotchas list built
from the mistakes this specific migration produces.

## Head Start

The one thing this migration makes worse is the opening response of a
new chat. The route handler answered out of a warm process; the agent
run has to be dequeued and booted first. That is the complaint the page
has to answer head on, so Head Start gets a full section rather than a
closing aside, plus a callout up top next to the "what changes" table so
nobody plans the migration without knowing it exists.

The section walks the four steps: splitting tool schemas away from tool
executes (the bundle-isolation constraint the whole feature rests on),
building the handler, mounting it back at `app/api/chat/route.ts` with
the original auth check wrapped around it, and the transport option.
Both server actions stay, because Head Start only owns the first turn.
Three gotchas go with it: a slow first turn without Head Start, Head
Start on but the route bundle still heavy, and the route timing out
because the handler holds the SSE response open for the whole turn
rather than just step 1.

The coding-agent prompt names Head Start as explicitly out of scope, so
an agent handed the migration does not attempt the tool split
unprompted.

Also fixes the `chat.headStart` example on `ai-chat/fast-starts`, which
set `stopWhen: stepCountIs(15)` after the spread.
`toStreamTextOptions()` pins `stopWhen` to `stepCountIs(1)`, so
overriding it makes the warm handler run steps the agent is supposed to
own (and `stepCountIs` was never imported in that snippet either).

## Migration prompt

The page also ships a copy-pasteable prompt for handing the migration to
a coding agent. It tells the agent to run `npx trigger.dev@latest
skills` first, so it picks up guidance version-pinned to the SDK
actually installed in the project, then read `quick-start.md`,
`frontend.md`, and `reference.md` (with `llms.txt` as the index) before
editing anything. The instructions are explicit about preserving the
existing model, prompt, and tool schemas rather than rewriting them.

Registered in `docs.json` under Agents, directly after Quick Start, so
it is picked up by the generated `llms.txt` and the per-page `.md`
variants.

Author: matt-aitken

docs/ai-chat/fast-starts.mdx

@@ -266,11 +266,14 @@ This is an **import-chain** problem, not a runtime one. A "we'll strip the execu
           ...helper.toStreamTextOptions({ tools: headStartTools }),
           model: anthropic("claude-sonnet-4-6"),
           system: "You are a helpful assistant.",
-          stopWhen: stepCountIs(15),
         }),
     });
     ```
 
+    <Warning>
+      Don't set `stopWhen` here. The spread pins it to `stepCountIs(1)`, and overriding it makes the handler run steps the agent is supposed to own — the handover then splices a stream that has already moved past step 1.
+    </Warning>
+
     <Tip>
       Use the **same model** on both sides (route handler and `chat.agent`) to avoid a tone or style shift between step 1 and step 2+. Your LLM provider keys stay server-side in your warm process — Trigger.dev never holds them in this design.
     </Tip>