Add a vector index to a Convex table and run a similarity search from an action using ctx.vectorSearch

Documented steps

1. In convex/schema.ts, chain .vectorIndex("by_embedding", { vectorField: "embedding", dimensions: 1536, filterFields: ["category"] }) onto the target table's defineTable(...) call.
2. Set dimensions to match your embedding model's output size (e.g. 1536 for OpenAI text-embedding-3-small); the value must be between 2 and 4096.
3. Optionally add filterFields (up to 16, dot notation supported for nested fields such as "properties.name") and/or staged: true for async backfill.
4. Deploy the schema so the vector index is built.
5. In an ACTION (not a query or mutation), compute or receive the query embedding as a number[] matching the index dimensions — typically by calling an embedding API from the action.
6. Call await ctx.vectorSearch("messages", "by_embedding", { vector: embedding, limit: 16, filter: (q) => q.eq("category", "news") }).
7. The call returns an array of objects each containing _id (the document ID) and _score (similarity between -1 and 1), ordered by similarity.
8. Fetch the full documents with the returned _ids via ctx.runQuery calling ctx.db.get(id), since vectorSearch returns only IDs and scores.
9. Store the embedding on the same document as the source text so a single fetch returns both.
10. Official docs: https://docs.convex.dev/search/vector-search