FastAPI booking backend: correct failures

FastAPI booking backend: correct failures and repeatable tests

Independent portfolio demo built with Python, FastAPI, and SQLite. The API exposes six documented routes and tests booking, cancellation, invalid inputs, missing records, and conflicting reservations. A conditional SQL update prevents claiming an already-booked slot; cancellation is idempotent. Source-derived OpenAPI documentation and an isolated test database make the project easy to inspect and run. The supplied validation record contains 26 passing tests. This is an offline demo using synthetic references, not a deployed clinic system.