fix(dailies): a built-in on another server's clock leaves the header countdown alone

Beyond the Rails rolls on Asia's reset, and the header took the soonest
reset of every chip, so a Europe NTE reader read "next reset in 1h" at
20:00 UTC when their day rolls in seven. The countdown now counts the
reader's own clocks. Found in the whole-branch review.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/client/components/Dailies.tsx

@@ -502,8 +502,12 @@ export function Dailies({
 
   // With mixed reset clocks there is no single "resets in", so the header
   // reports the next one to land and says that it is the next one.
-  const soonest = Math.min(...items.map((i) => i.resetsIn));
-  const mixed = new Set(items.map((i) => i.resetsIn)).size > 1;
+  // A built-in on another server's clock (`clock`) rolls a cycle, not the
+  // reader's day: counting it would announce a reset nothing daily follows.
+  const own = items.filter((i) => i.clock === undefined);
+  const clocks = own.length > 0 ? own : items;
+  const soonest = Math.min(...clocks.map((i) => i.resetsIn));
+  const mixed = new Set(clocks.map((i) => i.resetsIn)).size > 1;
   const open = items.find((i) => i.key === editing && i.goal?.measure === "amount");
 
   const { today, longer } = splitByCadence(items);

test/views.test.tsx

@@ -1471,6 +1471,22 @@ describe("weekly and monthly tasks in the dailies strip", () => {
     expect(item!.resetsIn).toBeGreaterThan(chore!.resetsIn);
   });
 
+  test("a clocked built-in does not move the header's reset countdown", () => {
+    const rails = {
+      id: "routine:nte:test-rails", game: "nte", title: "Beyond the Rails",
+      period: { unit: "cycle" as const, days: 14, from: "2026-10-22" },
+      measure: { kind: "days" as const, required: 1 }, clock: "asia" as const,
+    };
+    // 20:00 UTC: Europe's NTE day rolls at 03:00 UTC, seven hours off; Asia's in one.
+    const html = render(
+      <Dailies games={["nte"]} events={[]} region="europe" now={Date.parse("2026-10-21T20:00:00Z")}
+        showChores daysFor={() => []} onToggleDay={() => {}} tasks={[rails]}
+        taskStatusFor={() => undefined} />,
+    );
+    expect(html).not.toContain("next reset in");
+    expect(html).toMatch(/resets in (<!-- -->)?7h/);
+  });
+
   test("a cycle chip shows its days left, under a heading that names it", () => {
     const html = render(
       <Dailies games={["zzz"]} events={[]} region="europe" now={NOW} showChores={false}