Returns cited chunks with source filename and scores when the best dense
similarity clears the SIMILARITY_FLOOR gate. Below that floor, returns
status=no_relevant_sources with an empty chunk list — do not fabricate
an answer from weak matches.

Raises a tool error if the patient does not exist or the database is down —
never returns an empty success that could be mistaken for 'no appointments'.

date_to must be on or after date_from. Empty list with status=ok means no
confirmed appointments in that window — distinct from a database failure,
which raises a tool error.

Inserts a row into appointment_requests with status=pending and returns
pending_approval. A human must approve before anything lands on the
confirmed appointments calendar. Calling this twice creates two pending
requests; it never silently books.