perf(coderd): batch chat heartbeat queries into single UPDATE per interval (#24037)

## Summary

Replaces N per-chat heartbeat goroutines with a single centralized
heartbeat loop that issues one `UPDATE` per 30s interval for all running
chats on a worker.

## Problem

Each running chat spawned a dedicated goroutine that issued an
individual `UPDATE chats SET heartbeat_at = NOW() WHERE id = $1 AND
worker_id = $2 AND status = 'running'` query every 30 seconds. At 10,000
concurrent chats this produces **~333 DB queries/second** just for
heartbeats, plus ~333 `ActivityBumpWorkspace` CTE queries/second from
`trackWorkspaceUsage`.

## Solution

New `UpdateChatHeartbeats` (plural) SQL query replaces the old singular
`UpdateChatHeartbeat`:

```sql
UPDATE chats
SET    heartbeat_at = @now::timestamptz
WHERE  worker_id = @worker_id::uuid
  AND  status = 'running'::chat_status
RETURNING id;
```

A single `heartbeatLoop` goroutine on the `Server`:
1. Ticks every `chatHeartbeatInterval` (30s)
2. Issues one batch UPDATE for all registered chats
3. Detects stolen/completed chats via set-difference (equivalent of old
`rows == 0`)
4. Calls `trackWorkspaceUsage` for surviving chats

`processChat` registers an entry in the heartbeat registry instead of
spawning a goroutine.

## Impact

| Metric | Before (10K chats) | After (10K chats) |
|---|---|---|
| Heartbeat queries/sec | ~333 | ~0.03 (1 per 30s per replica) |
| Heartbeat goroutines | 10,000 | 1 |
| Self-interrupt detection | Per-chat `rows==0` | Batch set-difference |

---

> 🤖 Generated by Coder Agents

<details><summary>Implementation notes</summary>

- Uses `@now` parameter instead of `NOW()` so tests with `quartz.Mock`
can control timestamps.
- `heartbeatEntry` stores `context.CancelCauseFunc` + workspace state
for the centralized loop.
- `recoverStaleChats` is unaffected — it reads `heartbeat_at` which is
still updated.
- The old singular `UpdateChatHeartbeat` is removed entirely.
- `dbauthz` wrapper uses system-level `rbac.ResourceChat` authorization
(same pattern as `AcquireChats`).

</details>

coderd/database/dbauthz/dbauthz.go

@@ -5782,15 +5782,15 @@ func (q *querier) UpdateChatByID(ctx context.Context, arg database.UpdateChatByI
 	return q.db.UpdateChatByID(ctx, arg)
 }
 
-func (q *querier) UpdateChatHeartbeat(ctx context.Context, arg database.UpdateChatHeartbeatParams) (int64, error) {
-	chat, err := q.db.GetChatByID(ctx, arg.ID)
-	if err != nil {
-		return 0, err
+func (q *querier) UpdateChatHeartbeats(ctx context.Context, arg database.UpdateChatHeartbeatsParams) ([]uuid.UUID, error) {
+	// The batch heartbeat is a system-level operation filtered by
+	// worker_id. Authorization is enforced by the AsChatd context
+	// at the call site rather than per-row, because checking each
+	// row individually would defeat the purpose of batching.
+	if err := q.authorizeContext(ctx, policy.ActionUpdate, rbac.ResourceChat); err != nil {
+		return nil, err
 	}
-	if err := q.authorizeContext(ctx, policy.ActionUpdate, chat); err != nil {
-		return 0, err
-	}
-	return q.db.UpdateChatHeartbeat(ctx, arg)
+	return q.db.UpdateChatHeartbeats(ctx, arg)
 }
 
 func (q *querier) UpdateChatLabelsByID(ctx context.Context, arg database.UpdateChatLabelsByIDParams) (database.Chat, error) {

coderd/database/dbauthz/dbauthz_test.go

@@ -842,15 +842,15 @@ func (s *MethodTestSuite) TestChats() {
 		dbm.EXPECT().UpdateChatStatusPreserveUpdatedAt(gomock.Any(), arg).Return(chat, nil).AnyTimes()
 		check.Args(arg).Asserts(chat, policy.ActionUpdate).Returns(chat)
 	}))
-	s.Run("UpdateChatHeartbeat", s.Mocked(func(dbm *dbmock.MockStore, faker *gofakeit.Faker, check *expects) {
-		chat := testutil.Fake(s.T(), faker, database.Chat{})
-		arg := database.UpdateChatHeartbeatParams{
-			ID:       chat.ID,
+	s.Run("UpdateChatHeartbeats", s.Mocked(func(dbm *dbmock.MockStore, faker *gofakeit.Faker, check *expects) {
+		resultID := uuid.New()
+		arg := database.UpdateChatHeartbeatsParams{
+			IDs:      []uuid.UUID{resultID},
 			WorkerID: uuid.New(),
+			Now:      time.Now(),
 		}
-		dbm.EXPECT().GetChatByID(gomock.Any(), chat.ID).Return(chat, nil).AnyTimes()
-		dbm.EXPECT().UpdateChatHeartbeat(gomock.Any(), arg).Return(int64(1), nil).AnyTimes()
-		check.Args(arg).Asserts(chat, policy.ActionUpdate).Returns(int64(1))
+		dbm.EXPECT().UpdateChatHeartbeats(gomock.Any(), arg).Return([]uuid.UUID{resultID}, nil).AnyTimes()
+		check.Args(arg).Asserts(rbac.ResourceChat, policy.ActionUpdate).Returns([]uuid.UUID{resultID})
 	}))
 	s.Run("UpdateChatMessageByID", s.Mocked(func(dbm *dbmock.MockStore, faker *gofakeit.Faker, check *expects) {
 		chat := testutil.Fake(s.T(), faker, database.Chat{})