feat(tasks): a task can repeat every N days from a dated start

A third period, { unit: "cycle", days, from }, cut in day-key space like
weeks and months, so each game's per-server reset carries over. Tasks on
it are tallied and switched apart (showCycleTasks, on by default), show
the days left in their chip, and the lower row's heading now names the
periods it holds.

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

test/controls.test.tsx

@@ -1,4 +1,5 @@
 import { describe, expect, test } from "bun:test";
+import type { Task } from "../src/shared/task.ts";
 import { renderToStaticMarkup } from "react-dom/server";
 import { Controls, ownState, PerGameChips } from "../src/client/components/Controls.tsx";
 import { GameMetaProvider } from "../src/client/state/gameMeta.tsx";
@@ -33,6 +34,7 @@ const PREFS: Prefs = {
   showChores: true,
   showWeeklyTasks: true,
   showMonthlyTasks: true,
+  showCycleTasks: true,
   showCompleted: true,
   showIgnored: false,
   theme: "dark",
@@ -40,7 +42,12 @@ const PREFS: Prefs = {
   onboarded: true,
 };
 
-function render(prefs: Prefs, ignoredCount = 0, games = ["genshin", "hsr"]): string {
+function render(
+  prefs: Prefs,
+  ignoredCount = 0,
+  games = ["genshin", "hsr"],
+  tasks?: Task[],
+): string {
   return renderToStaticMarkup(
     <GameMetaProvider value={(id) => metaFor(id, {})}>
       <Controls
@@ -63,6 +70,7 @@ function render(prefs: Prefs, ignoredCount = 0, games = ["genshin", "hsr"]): str
           onEditGame: () => {},
           onRemoveGame: () => ({ removed: true, blockedBy: 0 }),
           onAddEvent: () => {},
+          ...(tasks === undefined ? {} : { tasks }),
         }}
       />
     </GameMetaProvider>,
@@ -415,9 +423,24 @@ describe("Controls: weekly and monthly tasks under the dailies", () => {
     expect(checkboxes(off).filter(Boolean).length).toBe(checkboxes(on).filter(Boolean).length - 1);
   });
 
+  test("a cycle task brings its own switch, which reads showCycleTasks", () => {
+    const AT = "2026-10-01T00:00:00.000Z";
+    const shiyu: Task = {
+      id: "mytask:dddddd4444", game: "hsr", title: "Shiyu Defense",
+      period: { unit: "cycle", days: 14, from: "2026-10-16" }, measure: { kind: "days", required: 1 },
+      at: AT, updatedAt: AT,
+    };
+    const on = render(PREFS, 0, undefined, [shiyu]);
+    expect(on).toContain("Show cycle tasks");
+    expect(on).not.toContain("Show weekly tasks");
+    const off = render({ ...PREFS, showCycleTasks: false }, 0, undefined, [shiyu]);
+    expect(checkboxes(off).filter(Boolean).length).toBe(checkboxes(on).filter(Boolean).length - 1);
+  });
+
   test("with no tasks at all, neither switch is offered", () => {
     const html = render(PREFS);
     expect(html).not.toContain("Show weekly tasks");
     expect(html).not.toContain("Show monthly tasks");
+    expect(html).not.toContain("Show cycle tasks");
   });
 });