feat(booth): rework Active Sessions + pay/exit modal around barrier re-open

Move the audited barrier re-open out of the inline Active-Sessions row button
and into the modal, and turn the modal's dead-ends into useful views.

- Remove the inline per-row "Open barrier" button. Clicking a row opens the
  modal, which carries the action.
- Modal recognizes a closed-within-grace transient (found && !open &&
  withinGrace) and shows the session view + Open barrier instead of dead-ending
  on "already closed" — the exact case (paid, barrier unconfirmed) that needs a
  re-pulse. Server reopenBarrier guard unchanged.
- Active-Sessions rows show a live grace-remaining countdown badge
  (exited - M:SS, 1s tick off graceExpiresAt) via new formatCountdown helper.
- Settled sessions show the ACTUAL sum paid (new SessionLookup.paidMinor,
  summed across payment events) instead of a flat "PAID" badge.
- A fully-closed (grace-expired) session's modal is no longer a dead-end: it
  shows a read-only review view (figures + paid amount + entry/exit snapshot
  strip) for dispute/audit review, with no pay/exit/open controls.

i18n sq+en parity kept; web build/lint/test green.

Claude-Session: https://claude.ai/code/session_01Xcm6ikLgGoCxxHrxtjkk5V

apps/web/src/lib/format.ts

@@ -22,6 +22,22 @@ export function formatDuration(fromIso: string, toIso: string): string {
   return h > 0 ? `${h}h ${m}m` : `${m}m`;
 }
 
+/** Remaining time until `untilIso`, as a live countdown: "M:SS" (or "H:MM:SS" past an
+ *  hour). Returns null once expired (or for a bad/empty input) so callers can drop the
+ *  badge. Pass `nowMs` (a ticking clock) to make it update each second. */
+export function formatCountdown(untilIso: string | null, nowMs: number = Date.now()): string | null {
+  if (!untilIso) return null;
+  const ms = Date.parse(untilIso) - nowMs;
+  if (!Number.isFinite(ms) || ms <= 0) return null;
+  const total = Math.ceil(ms / 1000);
+  const h = Math.floor(total / 3600);
+  const m = Math.floor((total % 3600) / 60);
+  const s = total % 60;
+  const ss = String(s).padStart(2, "0");
+  if (h > 0) return `${h}:${String(m).padStart(2, "0")}:${ss}`;
+  return `${m}:${ss}`;
+}
+
 /** 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 "—";