feat: show agent turn summary in agents sidebar (#24942)

Persists the agent-generated turn-end summary on `chats` and shows it as
the Agents sidebar subtitle when present, falling back to the model
name. Errors still take precedence.

> Mux is acting on Mike's behalf.

## What changes

**Storage.** New nullable `last_turn_summary` column on `chats`
(migration `000486`). New `UpdateChatLastTurnSummary` query normalizes
blank/whitespace input to `NULL`, preserves `updated_at` (so the chat
does not jump to the top of the sidebar on summary writes), and uses an
`expected_updated_at` stale-write guard so an older async summary cannot
overwrite a newer turn.

**Backend.** `coderd/x/chatd/chatd.go` decouples summary generation from
webpush. Generated summaries persist for completed parent turns even
when webpush is unconfigured or has no subscriptions. The same generated
text is reused as the webpush body when webpush is configured, so the
summary model is not called twice. Generic fallback push text is no
longer persisted; it clears any stale summary instead.
Error/interrupt/pending-action terminal paths clear `last_turn_summary`
for the latest turn.

**Frontend.** `AgentsSidebar.tsx` subtitle priority is now `errorReason
|| lastTurnSummary || modelName`, normalized via the existing
`asNonEmptyString` helper from `blockUtils.ts`.

## Tests

- `TestUpdateChatLastTurnSummary` (database): success,
whitespace-to-NULL, stale guard rejects, `updated_at` preserved.
- `TestUpdateLastTurnSummaryRejectsStaleWrites` (chatd internal): direct
stale-`expected_updated_at` test.
- `TestSuccessfulChatPersistsTurnSummaryWithoutWebPush`: persistence
works without webpush subscriptions.
- `TestSuccessfulChatSendsWebPushWithSummary`: same generated text
drives both DB and push body.
-
`TestSuccessfulChatSendsWebPushFallbackWithoutSummaryForEmptyAssistantText`:
fallback text is not persisted.
- `TestErroredChatClearsLastTurnSummaryAndSendsWebPush`: error path
clears the field.
- `TestInterruptChatDoesNotSendWebPushNotification`: interrupt path
clears the field, no push fires.
- `AgentsSidebar.test.tsx`: subtitle priority for summary-present,
error-wins, no-summary fallback, whitespace fallback.
- `AgentsSidebar.stories.tsx`: `ChatWithTurnSummary` and
`ChatWithTurnSummaryAndError`.

## Notes

- No backfill. Existing chats keep showing the model name until their
next turn completes.
- Parent chats only in this iteration; the field is rendered on any
`Chat` if a future change extends generation to children.
- Decoupling generation from webpush adds quickgen model calls for
completed parent turns that previously skipped generation when no
subscriptions existed. Existing parent-only, assistant-text-present,
`PushSummaryModel` configured, and bounded-timeout gates keep this
behavior bounded.

coderd/database/queries/chats.sql

@@ -632,6 +632,25 @@ WHERE
     id = @id::uuid
 RETURNING *;
 
+-- name: UpdateChatLastTurnSummary :execrows
+-- Updates the cached last completed turn summary for sidebar display.
+-- Empty or whitespace-only summaries are stored as NULL here so direct
+-- query callers cannot accidentally persist blank sidebar text.
+-- This intentionally preserves updated_at. The staleness guard relies on
+-- every new-turn query, such as UpdateChatStatus and AcquireChats, bumping
+-- updated_at. Future chat-field updates that do not bump updated_at can let
+-- stale summaries persist. If this query ever bumps updated_at, later
+-- goroutine summary writes will be rejected as stale.
+-- Two summary workers using the same freshness marker are last-write-wins.
+UPDATE chats
+SET
+    last_turn_summary = NULLIF(REGEXP_REPLACE(
+        sqlc.narg('last_turn_summary')::text, '^[[:space:]]+|[[:space:]]+$', '', 'g'
+    ), '')
+WHERE
+    id = @id::uuid
+    AND updated_at = @expected_updated_at::timestamptz;
+
 -- name: UpdateChatMCPServerIDs :one
 UPDATE
     chats