feat(coderd/chatd): structured chat error classification and retry hardening (#23275)

> **PR Stack**
> 1. #23351 ← `#23282`
> 2. #23282 ← `#23275`
> 3. **#23275** ← `#23349` *(you are here)*
> 4. #23349 ← `main`

---

## Summary

Extracts a structured error classification subsystem for agent chat
(`chatd`) so that retry and error payloads carry machine-readable
metadata — error kind, provider name, HTTP status code, and retryability
— instead of raw error strings.

This is the **backend half** of the error-handling work. The frontend
counterpart is in #23282.

## Changes

### New package: `coderd/chatd/chaterror/`

Canonical error classification — extracts error kind, provider, status
code, and user-facing message from raw provider errors. One source of
truth that drives both retry policy and stream payloads.

- **`kind.go`**: Error kind enum (`rate_limit`, `timeout`, `auth`,
`config`, `overloaded`, `unknown`).
- **`signals.go`**: Signal extraction — parses provider name, HTTP
status code, and retryability from error strings and wrapped types.
- **`classify.go`**: Classification logic — maps extracted signals to an
error kind.
- **`message.go`**: User-facing message templates keyed by kind +
signals.
- **`payload.go`**: Projectors that build `ChatStreamError` and
`ChatStreamRetry` payloads from a classified error.

### Modified

- **`codersdk/chats.go`**: Added `Kind`, `Provider`, `Retryable`,
`StatusCode` fields to `ChatStreamError` and `ChatStreamRetry`.
- **`coderd/chatd/chatretry/`**: Thinned to retry-policy only;
classification logic moved to `chaterror`.
- **`coderd/chatd/chatloop/`**: Added per-attempt first-chunk timeout
(60 s) via `guardedStream` wrapper — produces retryable
`startup_timeout` errors instead of hanging forever.
- **`coderd/chatd/chatd.go`**: Publishes normalized retry/error payloads
via `chaterror` projectors.

site/src/api/typesGenerated.ts

@@ -1763,7 +1763,26 @@ export const ChatStatuses: ChatStatus[] = [
  * ChatStreamError represents an error event in the stream.
  */
 export interface ChatStreamError {
+	/**
+	 * Message is the normalized, user-facing error message.
+	 */
 	readonly message: string;
+	/**
+	 * Kind classifies the error for consistent client rendering.
+	 */
+	readonly kind?: string;
+	/**
+	 * Provider identifies the upstream model provider when known.
+	 */
+	readonly provider?: string;
+	/**
+	 * Retryable reports whether the underlying error is transient.
+	 */
+	readonly retryable: boolean;
+	/**
+	 * StatusCode is the best-effort upstream HTTP status code.
+	 */
+	readonly status_code?: number;
 }
 
 // From codersdk/chats.go
@@ -1823,9 +1842,21 @@ export interface ChatStreamRetry {
 	 */
 	readonly delay_ms: number;
 	/**
-	 * Error is the error message from the failed attempt.
+	 * Error is the normalized error message from the failed attempt.
 	 */
 	readonly error: string;
+	/**
+	 * Kind classifies the retry reason for consistent client rendering.
+	 */
+	readonly kind?: string;
+	/**
+	 * Provider identifies the upstream model provider when known.
+	 */
+	readonly provider?: string;
+	/**
+	 * StatusCode is the best-effort upstream HTTP status code.
+	 */
+	readonly status_code?: number;
 	/**
 	 * RetryingAt is the timestamp when the retry will be attempted.
 	 */

site/src/pages/AgentsPage/components/AgentDetail/ChatContext.test.tsx

@@ -1570,7 +1570,7 @@ describe("useChatStore", () => {
 			mockSocket.emitData({
 				type: "error",
 				chat_id: chatID,
-				error: { message: "Rate limit exceeded" },
+				error: { message: "Rate limit exceeded", retryable: true },
 			});
 		});
 
@@ -1629,7 +1629,7 @@ describe("useChatStore", () => {
 			mockSocket.emitData({
 				type: "error",
 				chat_id: chatID,
-				error: { message: "  " },
+				error: { message: "  ", retryable: false },
 			});
 		});
 
@@ -1953,7 +1953,7 @@ describe("useChatStore", () => {
 			mockSocket.emitData({
 				type: "error",
 				chat_id: chatID,
-				error: { message: "Rate limit exceeded" },
+				error: { message: "Rate limit exceeded", retryable: true },
 			});
 		});
 
@@ -2750,7 +2750,7 @@ describe("updateSidebarChat via stream events", () => {
 			mockSocket.emitData({
 				type: "error",
 				chat_id: chatID,
-				error: { message: "something went wrong" },
+				error: { message: "something went wrong", retryable: false },
 			});
 		});
 
@@ -3026,7 +3026,7 @@ describe("updateSidebarChat via stream events", () => {
 			mockSocket.emitData({
 				type: "error",
 				chat_id: chatID,
-				error: { message: "something broke" },
+				error: { message: "something broke", retryable: false },
 			});
 		});