Build a filtered vector search in Qdrant using must/should/must_not/min_should with payload indexes so filters do not silently fall back to full scans

Documented steps

1. Compose a filter with logical clauses: {"must":[...],"should":[...],"must_not":[...]} — must = AND, should = OR, must_not = NOT. Clauses nest recursively.
2. Equality: {"key":"city","match":{"value":"London"}}. IN: {"match":{"any":["black","yellow"]}}. NOT IN: {"match":{"except":["black","yellow"]}}.
3. Numeric/datetime ranges: {"key":"price","range":{"gt":100,"lte":500}}. Datetime values must be RFC 3339 strings, e.g. "2023-02-08T10:49:00Z".
4. Geo filtering: geo_bounding_box (top_left/bottom_right), geo_radius (center + radius in meters), or geo_polygon (exterior ring plus optional interior rings).
5. For arrays of nested objects use {"nested":{"key":"diet","filter":{"must":[...]}}} rather than a dotted key, which matches across all array elements combined instead of within one element.
6. Require N of several optional conditions: "min_should":{"conditions":[...],"min_count":2}.
7. is_empty matches missing, null, or empty-array values; is_null matches only an explicit null. They are not interchangeable.
8. Pass the filter in the "filter" field of POST /collections/{collection_name}/points/query, /points/search, or /points/scroll.
9. Before filtering at scale, create the payload index: PUT /collections/{collection_name}/index with {"field_name":"city","field_schema":"keyword"}.
10. Confirm the index exists by checking payload_schema in GET /collections/{collection_name}.
11. Reference: https://qdrant.tech/documentation/search/filtering/
12. Reference: https://qdrant.tech/documentation/manage-data/indexing/