docs(ai-chat): add an anatomy entry page and reorder building agents

The Building agents group opened with the long How it works mechanics
page, which is the wrong first step after the Quick Start. A new
Anatomy page now leads the group: the three moving parts (agent task,
session, frontend transport), one annotated chat.agent example where
each region names the page that covers it, and a routing table for the
group. No setup steps, explicitly skippable.

How it works moves to the end of the group as the depth payoff, the
position peers (Clerk, LangGraph) give their internals pages. Also
registers the Custom agents page at the bottom of the group.

Author: ericallam

docs/ai-chat/anatomy.mdx

@@ -0,0 +1,71 @@
+---
+title: "Anatomy of an agent"
+sidebarTitle: "Anatomy"
+description: "The moving parts of a chat agent — the agent task, the session, the frontend transport — and which page covers each."
+---
+
+import RcBanner from "/snippets/ai-chat-rc-banner.mdx";
+
+<RcBanner />
+
+**A chat agent is three parts: a long-lived agent task that runs the turn loop, a durable Session carrying messages in and the response stream out, and a frontend transport that plugs the session into `useChat`.** The pages in this section each own one part of that picture. This page is the map — if you'd rather read mechanics end to end, skip to [How it works](/ai-chat/how-it-works).
+
+```mermaid
+flowchart LR
+  FE["Frontend<br/>useChat + transport"] -- "user messages" --> IN([Session .in])
+  IN --> AGENT["Agent task<br/>turn loop + hooks"]
+  AGENT --> OUT([Session .out])
+  OUT -- "streamed response" --> FE
+```
+
+Everything below maps onto one annotated agent:
+
+```ts trigger/my-agent.ts
+import { chat } from "@trigger.dev/sdk/ai";
+import { streamText, stepCountIs } from "ai";
+import { anthropic } from "@ai-sdk/anthropic";
+
+export const myAgent = chat.agent({
+  id: "my-agent",
+
+  // Tools declared on the config survive history re-conversion
+  // across turns — see Tools.
+  tools: { searchDocs },
+
+  // Hooks fire around each turn: validation, persistence,
+  // post-turn work — see Lifecycle hooks.
+  onTurnComplete: async ({ responseMessage }) => {
+    await db.messages.save(responseMessage);
+  },
+
+  // The turn loop. Messages arrive accumulated; you stream back.
+  // Options, levels, and alternatives — see Backend.
+  run: async ({ messages, tools, signal }) =>
+    streamText({
+      ...chat.toStreamTextOptions({ tools }),
+      model: anthropic("claude-sonnet-4-5"),
+      messages,
+      abortSignal: signal,
+      stopWhen: stepCountIs(15),
+    }),
+});
+```
+
+The frontend side is one hook — `useTriggerChatTransport` connects `useChat` to the agent's session, no API routes ([Frontend](/ai-chat/frontend)). Underneath, the conversation lives on a [Session](/ai-chat/sessions): a pair of durable streams keyed on your `chatId` that survives refreshes, deploys, and run boundaries.
+
+## Where each part is covered
+
+| Part                                                  | Page                                           |
+| ----------------------------------------------------- | ---------------------------------------------- |
+| `chat.agent()` options, the turn loop, piping         | [Backend](/ai-chat/backend)                    |
+| Hooks around each turn (`onTurnComplete`, hydration)  | [Lifecycle hooks](/ai-chat/lifecycle-hooks)    |
+| Declaring tools, typed payloads, `toModelOutput`      | [Tools](/ai-chat/tools)                        |
+| `useChat` wiring, tokens, starting sessions           | [Frontend](/ai-chat/frontend)                  |
+| Driving a chat from your server instead of a browser  | [Server-side chat](/ai-chat/server-chat)       |
+| The durable substrate under every agent               | [Sessions](/ai-chat/sessions)                  |
+| Per-run typed state inside the loop                   | [chat.local](/ai-chat/chat-local)              |
+| Type-safe payloads, client data, and messages         | [Types](/ai-chat/types)                        |
+| Building without the managed lifecycle                | [Custom agents](/ai-chat/custom-agents)        |
+| End-to-end mechanics: what survives a refresh and why | [How it works](/ai-chat/how-it-works)          |
+
+Beyond this section: [Features](/ai-chat/fast-starts) covers opt-in capabilities (Head Start, compaction, steering, actions), and [Patterns](/ai-chat/patterns/sub-agents) covers production recipes (sub-agents, HITL approvals, persistence, recovery).

docs/docs.json

@@ -104,15 +104,17 @@
               {
                 "group": "Building agents",
                 "pages": [
-                  "ai-chat/how-it-works",
+                  "ai-chat/anatomy",
                   "ai-chat/backend",
                   "ai-chat/lifecycle-hooks",
                   "ai-chat/tools",
                   "ai-chat/frontend",
                   "ai-chat/server-chat",
                   "ai-chat/sessions",
                   "ai-chat/chat-local",
-                  "ai-chat/types"
+                  "ai-chat/types",
+                  "ai-chat/custom-agents",
+                  "ai-chat/how-it-works"
                 ]
               },
               {