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.

codersdk/chats.go

@@ -778,7 +778,16 @@ type ChatStreamStatus struct {
 
 // ChatStreamError represents an error event in the stream.
 type ChatStreamError struct {
+	// Message is the normalized, user-facing error message.
 	Message string `json:"message"`
+	// Kind classifies the error for consistent client rendering.
+	Kind string `json:"kind,omitempty"`
+	// Provider identifies the upstream model provider when known.
+	Provider string `json:"provider,omitempty"`
+	// Retryable reports whether the underlying error is transient.
+	Retryable bool `json:"retryable"`
+	// StatusCode is the best-effort upstream HTTP status code.
+	StatusCode int `json:"status_code,omitempty"`
 }
 
 // ChatStreamRetry represents an auto-retry status event in the stream.
@@ -788,8 +797,14 @@ type ChatStreamRetry struct {
 	Attempt int `json:"attempt"`
 	// DelayMs is the backoff delay in milliseconds before the retry.
 	DelayMs int64 `json:"delay_ms"`
-	// Error is the error message from the failed attempt.
+	// Error is the normalized error message from the failed attempt.
 	Error string `json:"error"`
+	// Kind classifies the retry reason for consistent client rendering.
+	Kind string `json:"kind,omitempty"`
+	// Provider identifies the upstream model provider when known.
+	Provider string `json:"provider,omitempty"`
+	// StatusCode is the best-effort upstream HTTP status code.
+	StatusCode int `json:"status_code,omitempty"`
 	// RetryingAt is the timestamp when the retry will be attempted.
 	RetryingAt time.Time `json:"retrying_at" format:"date-time"`
 }