[api] fix ban duration display

apps/www/src/staff.ts

@@ -216,10 +216,11 @@ function banExpiry(
  * ROOM ban must never send it (`rooms` sends `IsBan: false` and is enforced by refusing the
  * room), because the client cannot tell the two apart and shows a game-wide ban screen.
  *
- * Its contents are {@link banBlockDetails} — the same `ReportCategory`, `Message` and the
- * `Duration`/`TimeoutStartedAt` pair `moderationBlockDetails` answers for this ban — so the
- * screen a player sees mid-session is the screen they see when they next sign in, not a
- * generic "banned" with no length.
+ * Its contents are {@link banBlockDetails} — the same `ReportCategory`, `Message` and
+ * `Duration` `moderationBlockDetails` answers for this ban — so the screen a player sees
+ * mid-session is the screen they see when they next sign in, not a generic "banned" with no
+ * length. `Duration` is the seconds LEFT, and this frame goes out the instant the ban is
+ * handed down, so here that is the ban's whole span; every later sign-in gets less.
  *
  * Sent to anyone ONLINE, not only to a player standing in an instance: someone in a menu is
  * as banned as someone in a room. `GameSessionId` is their instance, or 0 when they are in

apps/www/src/test/integration/api.test.ts

@@ -1280,14 +1280,16 @@ it('throws a banned player out of the instance they are standing in', async () =
 	expect(frames[0].data.GameSessionId).toBe(77001)
 
 	// The SAME ban the sign-in screen describes, not a generic one: its category, message and
-	// the Duration/TimeoutStartedAt pair, three days from when it was handed down.
+	// `Duration` — the seconds LEFT, which at the instant the ban is handed down is the whole
+	// three days. `TimeoutStartedAt` is not paired with it by the client and stays null.
 	const banned = await getReportById(env.DB, report.id)
 	expect(frames[0].data).toMatchObject({
 		ReportCategory: banned!.report_category,
 		Message: 'Rule violation',
-		TimeoutStartedAt: banned!.banned_at,
-		Duration: 3 * 86_400,
+		TimeoutStartedAt: null,
 	})
+	expect(frames[0].data.Duration).toBeGreaterThan(3 * 86_400 - 5)
+	expect(frames[0].data.Duration).toBeLessThanOrEqual(3 * 86_400)
 
 	// And they are out of that instance — moved into their own DORM, not deleted: `match`
 	// lets a banned player matchmake there and nowhere else, so it is where they read the