feat(carwash): Car Wash v1 + per-till shifts + site-level pay-at + till access by module permission

Car Wash — the pilot venue module (wiki/decisions/venue-modules.md):
- Master data (categories × services price matrix) at /setup/carwash; the desk at /wash
  (ticket lookup → order; open queue oldest-first: Done / Paid cash / Paid card / Void;
  Finished list). Orders freeze names + price; their life is signed (carwash_order,
  carwash_payment). Migration 0027.
- Where money is taken is a SITE setting (carwash_config.pay_at, migration 0028, signed
  config_change on a flip) — no per-order radio; a stale client is refused (409).
- Core seams: PayStation charge providers (a booth-paid wash rides the parking payment as
  chargeLines) + applyValidation() shared with the merchant route. A bay-paid, done wash
  signs the $0 parking payment so the exit reader releases the car.
- "Parking discount" modes for the wash: free while the wash runs (+ tolerance) and wash
  price off the fee (floored at 0), resolved at done and anchored at the order's intake
  (the entry-anchored version comped a 74-day stay); typed-amount and percent hidden for
  the wash. Long durations render y/d/h/m.

Tills — a shift belongs to a till, not the site (wiki/concepts/shift.md §Tills):
- TillId booth|carwash; every money event names its till (absent = booth, so the chain
  re-folds identically). ShiftService is per till: single-open, folds, X/Z-reports,
  vouchers, carry-forward. A bay payment needs the carwash shift.
- Working a till needs that till's module permission (manifest tillPermission; 403
  till_forbidden); /api/shift/tills lists only the role's tills.
- Web: ShiftButton per till (header = booth, wash desk = carwash); shift hub lists every
  open shift with till badges + filter; drawer hub switches tills.

Modules: landing per module (index route resolves booth → module landing → shifts →
profile); guards bounce to "/", /booth needs session:read.

Tests: carwash e2e suite (settings, intake, booth/bay paths, modes, void, gate, pay-at
policy, till permissions), 6 per-till shift tests; suite green (1 pre-existing flaky
backup test under the parallel run).

Claude-Session: https://claude.ai/code/session_01FWncR69HgGPuei1dLrW3cU

apps/web/src/lib/format.ts

@@ -16,10 +16,24 @@ export function formatMoney(amountMinor: number, currency: string): string {
 export function formatDuration(fromIso: string, toIso: string): string {
   const ms = Date.parse(toIso) - Date.parse(fromIso);
   if (!Number.isFinite(ms) || ms < 0) return "—";
-  const mins = Math.floor(ms / 60_000);
-  const h = Math.floor(mins / 60);
+  return formatMinutesLong(Math.floor(ms / 60_000));
+}
+
+/** "Xy Xd Xh Xm" with the leading zero units dropped — a stay of 1797h reads as
+ *  "74d 21h 23m", not a wall of hours (a stale/forgotten ticket is a real case on a
+ *  booth; the number should still be readable at a glance). Years only past 365 days. */
+export function formatMinutesLong(totalMinutes: number): string {
+  const mins = Math.max(0, Math.floor(totalMinutes));
+  const y = Math.floor(mins / (365 * 24 * 60));
+  const d = Math.floor((mins % (365 * 24 * 60)) / (24 * 60));
+  const h = Math.floor((mins % (24 * 60)) / 60);
   const m = mins % 60;
-  return h > 0 ? `${h}h ${m}m` : `${m}m`;
+  const parts: string[] = [];
+  if (y > 0) parts.push(`${y}y`);
+  if (y > 0 || d > 0) parts.push(`${d}d`);
+  if (y > 0 || d > 0 || h > 0) parts.push(`${h}h`);
+  parts.push(`${m}m`);
+  return parts.join(" ");
 }
 
 /** Remaining time until `untilIso`, as a live countdown: "M:SS" (or "H:MM:SS" past an
@@ -41,9 +55,7 @@ export function formatCountdown(untilIso: string | null, nowMs: number = Date.no
 /** Human duration from whole minutes, e.g. 134 → "2h 14m", 47 → "47m", 0 → "0m". */
 export function formatMinutes(mins: number): string {
   if (!Number.isFinite(mins) || mins < 0) return "—";
-  const m = Math.round(mins);
-  const h = Math.floor(m / 60);
-  return h > 0 ? `${h}h ${m % 60}m` : `${m}m`;
+  return formatMinutesLong(Math.round(mins));
 }
 
 /** Calendar-day difference (local) between two dates: 0 = same day, 1 = d is one day