Set up pgvector in Supabase and run nearest-neighbor similarity search

Steps

1. Enable the pgvector extension in the Supabase SQL editor: `CREATE EXTENSION IF NOT EXISTS vector;`.
2. Add a vector column to your table: `ALTER TABLE documents ADD COLUMN embedding vector(1536);` (dimension must match your embedding model output).
3. Insert rows with embeddings generated by your embedding API: `UPDATE documents SET embedding = '[0.1, 0.2, ...]'::vector WHERE id = 1;`.
4. Create an HNSW index for approximate nearest-neighbor search: `CREATE INDEX ON documents USING hnsw (embedding vector_cosine_ops);`.
5. Query for the top-k nearest neighbors: `SELECT id, content, embedding <=> '[...]'::vector AS distance FROM documents ORDER BY distance LIMIT 10;`