fix: discover nested vector columns by default (#3423)

LanceDB default vector column discovery only considered top-level
fields, so tables with a single nested vector leaf still required users
to pass an explicit field path. This updates Rust and Python discovery
to recurse into struct fields, return canonical field paths, and
preserve actionable errors when no default or multiple defaults exist.

The explicit nested path flow for index creation and search remains
supported across Rust, Python, and Node, with regression coverage for
single nested vector leaves, multiple candidate leaves, and schemas
without vector leaves.

Closes #3405.

nodejs/__test__/table.test.ts

@@ -28,6 +28,7 @@ import {
   List,
   Schema,
   SchemaLike,
+  Struct,
   Type,
   Uint8,
   Utf8,
@@ -780,6 +781,113 @@ describe("When creating an index", () => {
     expect(indices2.length).toBe(0);
   });
 
+  it("should create and search a nested vector index", async () => {
+    const db = await connect(tmpDir.name);
+    const nestedSchema = new Schema([
+      new Field("id", new Int32(), true),
+      new Field(
+        "image",
+        new Struct([
+          new Field(
+            "embedding",
+            new FixedSizeList(2, new Field("item", new Float32(), true)),
+            true,
+          ),
+        ]),
+        true,
+      ),
+    ]);
+    const nestedTable = await db.createTable(
+      "nested_vector",
+      makeArrowTable(
+        Array.from({ length: 300 }, (_, id) => ({
+          id,
+          image: { embedding: [id, id + 1] },
+        })),
+        { schema: nestedSchema },
+      ),
+    );
+
+    await nestedTable.createIndex("image.embedding", {
+      name: "image_embedding_idx",
+    });
+    const indices = await nestedTable.listIndices();
+    expect(indices).toContainEqual({
+      name: "image_embedding_idx",
+      indexType: "IvfPq",
+      columns: ["image.embedding"],
+    });
+
+    const explicit = await nestedTable
+      .query()
+      .nearestTo([0.0, 1.0])
+      .column("image.embedding")
+      .limit(1)
+      .toArray();
+    const inferred = await nestedTable
+      .query()
+      .nearestTo([0.0, 1.0])
+      .limit(1)
+      .toArray();
+    expect(inferred[0].id).toEqual(explicit[0].id);
+  });
+
+  it("should report multiple nested vector candidates", async () => {
+    const db = await connect(tmpDir.name);
+    const nestedSchema = new Schema([
+      new Field(
+        "image",
+        new Struct([
+          new Field(
+            "embedding",
+            new FixedSizeList(2, new Field("item", new Float32(), true)),
+            true,
+          ),
+        ]),
+        true,
+      ),
+      new Field(
+        "text",
+        new Struct([
+          new Field(
+            "embedding",
+            new FixedSizeList(2, new Field("item", new Float32(), true)),
+            true,
+          ),
+        ]),
+        true,
+      ),
+    ]);
+    const nestedTable = await db.createTable(
+      "multiple_nested_vectors",
+      makeArrowTable(
+        [
+          {
+            image: { embedding: [0.0, 1.0] },
+            text: { embedding: [2.0, 3.0] },
+          },
+        ],
+        { schema: nestedSchema },
+      ),
+    );
+
+    await expect(
+      nestedTable.query().nearestTo([0.0, 1.0]).limit(1).toArray(),
+    ).rejects.toThrow(/image\.embedding.*text\.embedding/);
+  });
+
+  it("should report when no default vector column exists", async () => {
+    const db = await connect(tmpDir.name);
+    const noVectorTable = await db.createTable(
+      "no_vector",
+      makeArrowTable([{ id: 0, label: "cat" }]),
+    );
+
+    await expect(
+      noVectorTable.query().nearestTo([0.0, 1.0]).limit(1).toArray(),
+    ).rejects.toThrow(/No vector column/);
+  });
+
   it("should wait for index readiness", async () => {
     // Create an index and then wait for it to be ready
     await tbl.createIndex("vec");