fix(db): track the time-zone pin's failure log as background work

The pin's SET on connect runs detached; its failure line now registers
with the background-task tracker like every other detached writer. The
coach thread test reads the new budget reset copy.

src/components/insights/coach-panel/__tests__/message-thread.test.tsx

@@ -699,7 +699,7 @@ describe("<MessageThread>", () => {
       />,
     );
     expect(html).toContain(
-      "Daily limit reached. The budget refreshes at midnight UTC.",
+      "Daily limit reached. The budget refreshes at midnight in your time zone.",
     );
     // v1.4.33 IW7 — fallback copy rewritten ("AI provider" -> "Insights
     // provider"). Both old and new strings should be absent here when

src/lib/db-session.ts

@@ -6,6 +6,8 @@
  */
 import type { Pool, PoolClient } from "pg";
 
+import { trackBackgroundTask } from "@/lib/logging/background-tasks";
+
 /**
  * Whether the app may send the libpq `options` startup parameter at all.
  *
@@ -62,8 +64,12 @@ export function timeZoneSessionOptions(): string | undefined {
 export function pinTimeZoneOnConnect(pool: Pool): void {
   if (!sessionOptionsDisabled()) return;
   pool.on("connect", (client: PoolClient) => {
-    client.query(SET_SESSION_TIME_ZONE).catch((err: unknown) => {
-      console.error("[db] Could not pin the session time zone:", err);
-    });
+    trackBackgroundTask(
+      client.query(SET_SESSION_TIME_ZONE).catch((err: unknown) => {
+        // The boot check reports a session that is not in UTC; this names
+        // the cause when the statement itself failed.
+        console.error("[db] Could not pin the session time zone:", err);
+      }),
+    );
   });
 }