[Frontend] Implement the missing appointmentsAPI.createAppointment contract

## Problem

BookingModal calls createAppointment even though AppointmentsAPI does not expose that method.

## Relevant code

`src/components/Appointments/BookingModal.tsx, src/lib/api/appointmentsAPI.ts`

## Proposed scope

Define the request/response types, implement the API call, map backend errors, and test successful and rejected bookings.

## Acceptance criteria

- [ ] The reported behavior is reproduced or characterized with a focused automated test before the fix.
- [ ] The implementation satisfies the proposed scope without weakening TypeScript, lint, authorization, privacy, or error handling.
- [ ] Success, empty/loading where applicable, failure, and boundary cases are covered.
- [ ] Existing related tests pass and new regression coverage is included.
- [ ] User-facing behavior remains accessible by keyboard and at mobile viewport sizes where UI is affected.
- [ ] Documentation is updated when the change alters configuration, contracts, security assumptions, or contributor workflow.

## Contributor notes

Base the work on the latest `main` branch. Keep unrelated refactors out of the pull request and include screenshots or recordings for visible changes. Never use real pet, medical, contact, wallet, or credential data in fixtures.

Start with src/components/Appointments/BookingModal.tsx and src/lib/api/appointmentsAPI.ts, then inspect the existing appointment API patterns and backend contract. Reproduce or characterize the missing createAppointment behavior with a focused test, implement the typed request and response handling, and cover successful, rejected, loading or empty, and boundary cases without weakening authorization, privacy, accessibility, or mobile behavior.

Written by the indexing model from the issue text.