refactor(booking): cache guest page formatters and reuse the slots query key

[tyler-dane]

Summary

Three behavior-preserving cleanups left by the booking work packages (#3022-#3045). No user-visible change; no new exports beyond one query-key prefix.

1. public-booking.format.ts cached one formatter and rebuilt six. The file already kept a per-timezone cache for the date-key formatter, with a comment stating that constructing Intl.DateTimeFormat is the expensive part. The other six formatters ignored that and constructed a fresh one on every call, and they are the hot ones: formatBookingSlotTime runs once per open slot, formatBookingMonthDayLabel once per day cell, and listBookingWeekdayHeadings builds 14 formatters per call. Generalized the existing cache into a perTimeZoneFormatter helper and routed all seven through it, which also removes six near-identical option literals. Cache keys are IANA zones already validated by validatePublicBookingSearch, so it stays bounded.

2. PublicBookingMonthGrid formatted labels it threw away. aria-label was computed for every cell before the !day.available early return discarded it, so most of a month's ~35-42 labels were built and dropped. Moved it to where it is used.

3. public-booking.query.ts hand-wrote a query key. The reservation mutation invalidated slots with a literal ["public-booking", "slots", slug] instead of publicBookingQueryKeys -- the only such call site in the web package, and one that would silently stop matching if the key factory changed shape. Added a slotsAll prefix, built slots from it, and invalidated through it. The page and reservation queries also carried the same not-found retry predicate verbatim twice; named it retryUnlessNotFound once.

Simplicity

Net reduction. The formatter change removes six duplicated option literals and the bespoke dateKeyFormatters map in favor of one 15-line helper; the query change removes a duplicated 6-line predicate and a magic key array. Nothing new is abstracted that did not already exist in the file: perTimeZoneFormatter is the existing dateKeyFormatter cache with the option set lifted out.

Automated validation

bun run verify selected the web package and passed test:web, type-check, lint, and knip. Because the change touches rendered guest-page output, the Playwright suites verify skipped for a missing browser were run explicitly after installing Chromium: all 30 e2e/booking specs pass, and the booking a11y specs pass.

bun test:a11y also surfaces 6 failures in app-a11y.spec.ts and datepicker-a11y.spec.ts (week view, event forms, sidebar datepicker). These are pre-existing and unrelated: re-running those two spec files on a clean main (00f3e00) with this branch stashed reproduces the same 6 failures. They are calendar-app color-contrast checks that touch no booking code.

Independent review

No /review handoff for this change. Self-review notes on the risky edge: formatGuestTimeZoneLabel depends on Intl throwing for an invalid timezone, and the construction still happens inside its try (nothing is cached on throw), so the fallback-to-raw-zone behavior is preserved. Intl option property order is not significant, so spreading ...options before timeZone is equivalent to the previous literals.

Test plan

bun install
bun type-check
bun lint
bun test:web -- packages/web/src/booking/     # 126 pass, 0 fail
bun run verify                                # test:web, type-check, lint, knip passed
bunx playwright install chromium
bun test:e2e -- e2e/booking/                  # 30 passed
bun test:a11y                                 # 18 passed; 6 pre-existing app/datepicker failures, reproduced on clean main

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