POS Section Rework — Slice 4 (prod)

10/10 prod test PASS on get-coffee (Pro) + lumiere-coffee (Starter). 1 commit, no migration.

Part A — prod DAO probe: the shipped listSessions against get-coffee's real sessions — total matches a raw COUNT, the page is newest-first, the register filter returns 0 out-of-register rows, and the Theoretical Closing column matches an independent recompute from cafe.orders/order_payments/cash_movements.
Part B/C — Playwright on the deployed Worker: /cafe/pos/sessions renders the table inside the POS shell (rail still mounted); the register <select> filter navigates with ?register= and re-renders; prev/next pagination advances to ?page=2; verified on get-coffee (Pro) and lumiere-coffee (Starter, 364 sessions → paginated).
One shared formula path — the per-session money math was extracted into aggregateSessionMetricsBySessionIds, so the Sessions page's Theoretical Closing and the landing cards' come from the same helper. fetchLatestSessionSummaries rewired to it — behaviour unchanged (regression-checked at Gate 1 + the r1-2-landing/r7 suites below).
Commit 1a73e77 — 1 edited + 2 new files, no migration.

Prod test — 10/10

✓ Part A — listSessions probe ran clean against get-coffee prod DB
✓ listSessions.total matches a raw COUNT; page is newest-first
✓ Register filter scopes correctly — 0 out-of-register rows
✓ theoreticalClosing column matches an independent prod recompute
✓ get-coffee — SSO login
✓ /cafe/pos/sessions renders the table inside the POS shell
✓ Pagination — Next advances to page 2 (if get-coffee has >1 page)
✓ Register filter — selecting a register navigates with ?register= and re-renders
✓ lumiere-coffee — SSO login
✓ lumiere-coffee (Starter) — /cafe/pos/sessions renders the table + pagination

59/59 regression green — no regressions from this push. 69/69 effective (10 Slice 4 prod + 59 regression).

test-phase1-prod.mjs — route/SSO smoke	11/11
test-phase2-sso-outdoor-prod.mjs	6/6
test-phase2-cafe-multishop-prod.mjs	6/6
test-m1-prod.mjs — shop scoping	10/10
test-r7-prod.mjs — dashboard + manager-live drawer	14/14
test-r8-prod.mjs — auth/security	4/4
test-r1-2-landing-prod.mjs — POS landing	8/8

phase1 flaked once again on the SSO hop (URL landed on / not /cafe/dashboard) — green on solo retry; the same known cold-start flake seen in Slices 2 & 3, and Slice 4 touched only cafe_sessions.ts + pos/sessions/* — nothing near /dashboard or routing/SSO.

Files touched — commit 1a73e77

nix-cafe (1 edited + 2 new, no migration):
  lib/db/cafe_sessions.ts                        + aggregateSessionMetricsBySessionIds (shared helper)
                                                 + listSessions / SessionListRow / SessionListResult
                                                 fetchLatestSessionSummaries rewired to the helper
  app/(authed)/pos/sessions/page.tsx             placeholder → real page (listSessions + register filter)
  app/(authed)/pos/sessions/sessions-client.tsx  new — table + mobile cards + filter + pagination

Arc progress — 4 of 6 slices shipped

Slice 1 ✅ session-scoped summary data layer
Slice 2 ✅ landing card UI rework
Slice 3 ✅ master-detail submenu shell
Slice 4 ✅ Sessions history page  ← this
Slice 5 — Registers + Orders relocation cleanup + section permission gating
          (/pos/sessions currently needs reports.view on top of the
          layout's pos.view; /pos/registers inherits settings.view —
          Slice 5 settles all of it + drops the Settings nav row +
          redirect stubs)