feat(worker): server-authoritative Stopwatch screen with active-session recovery

apps/worker/src/lib/stopwatch.test.ts

@@ -0,0 +1,19 @@
+import { describe, expect, it } from 'vitest';
+import { elapsedSeconds, formatTime } from './stopwatch';
+
+describe('stopwatch logic', () => {
+  it('formats seconds as HH:MM:SS', () => {
+    expect(formatTime(0)).toBe('00:00:00');
+    expect(formatTime(65)).toBe('00:01:05');
+    expect(formatTime(3661)).toBe('01:01:01');
+  });
+
+  it('computes elapsed seconds since start excluding paused time', () => {
+    expect(elapsedSeconds(1000, 6000, 0)).toBe(5);
+    expect(elapsedSeconds(1000, 6000, 2000)).toBe(3);
+  });
+
+  it('never returns a negative elapsed value', () => {
+    expect(elapsedSeconds(5000, 1000, 0)).toBe(0);
+  });
+});

apps/worker/src/lib/stopwatch.ts

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+// Pure timing helpers for the Stopwatch screen — server-authoritative elapsed.
+// Elapsed is computed from the server start_time (wall-clock), not a tick counter,
+// so it survives backgrounding. Pause accumulates paused time client-side.
+
+export function formatTime(totalSeconds: number): string {
+  const s = Math.max(0, Math.floor(totalSeconds));
+  const h = Math.floor(s / 3600);
+  const m = Math.floor((s % 3600) / 60);
+  const sec = s % 60;
+  return `${String(h).padStart(2, '0')}:${String(m).padStart(2, '0')}:${String(sec).padStart(2, '0')}`;
+}
+
+// elapsed seconds since startMs, excluding accumulated paused ms, evaluated at nowMs.
+export function elapsedSeconds(startMs: number, nowMs: number, pausedMs: number): number {
+  return Math.max(0, Math.floor((nowMs - startMs - pausedMs) / 1000));
+}