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/queries.sql.go

@@ -6615,30 +6615,49 @@ func (q *sqlQuerier) UpdateChatByID(ctx context.Context, arg UpdateChatByIDParam
 	return i, err
 }
 
-const updateChatHeartbeat = `-- name: UpdateChatHeartbeat :execrows
+const updateChatHeartbeats = `-- name: UpdateChatHeartbeats :many
 UPDATE
     chats
 SET
-    heartbeat_at = NOW()
+    heartbeat_at = $1::timestamptz
 WHERE
-    id = $1::uuid
-    AND worker_id = $2::uuid
+    id = ANY($2::uuid[])
+    AND worker_id = $3::uuid
     AND status = 'running'::chat_status
+RETURNING id
 `
 
-type UpdateChatHeartbeatParams struct {
-	ID       uuid.UUID `db:"id" json:"id"`
-	WorkerID uuid.UUID `db:"worker_id" json:"worker_id"`
+type UpdateChatHeartbeatsParams struct {
+	Now      time.Time   `db:"now" json:"now"`
+	IDs      []uuid.UUID `db:"ids" json:"ids"`
+	WorkerID uuid.UUID   `db:"worker_id" json:"worker_id"`
 }
 
-// Bumps the heartbeat timestamp for a running chat so that other
-// replicas know the worker is still alive.
-func (q *sqlQuerier) UpdateChatHeartbeat(ctx context.Context, arg UpdateChatHeartbeatParams) (int64, error) {
-	result, err := q.db.ExecContext(ctx, updateChatHeartbeat, arg.ID, arg.WorkerID)
+// Bumps the heartbeat timestamp for the given set of chat IDs,
+// provided they are still running and owned by the specified
+// worker. Returns the IDs that were actually updated so the
+// caller can detect stolen or completed chats via set-difference.
+func (q *sqlQuerier) UpdateChatHeartbeats(ctx context.Context, arg UpdateChatHeartbeatsParams) ([]uuid.UUID, error) {
+	rows, err := q.db.QueryContext(ctx, updateChatHeartbeats, arg.Now, pq.Array(arg.IDs), arg.WorkerID)
 	if err != nil {
-		return 0, err
+		return nil, err
 	}
-	return result.RowsAffected()
+	defer rows.Close()
+	var items []uuid.UUID
+	for rows.Next() {
+		var id uuid.UUID
+		if err := rows.Scan(&id); err != nil {
+			return nil, err
+		}
+		items = append(items, id)
+	}
+	if err := rows.Close(); err != nil {
+		return nil, err
+	}
+	if err := rows.Err(); err != nil {
+		return nil, err
+	}
+	return items, nil
 }
 
 const updateChatLabelsByID = `-- name: UpdateChatLabelsByID :one