ci(node): run examples in CI (#1796)

This is done as setup for a PR that will fix the OpenAI dependency
issue.

 * [x] FTS examples
 * [x] Setup mock openai
 * [x] Ran `npm audit fix`
 * [x] sentences embeddings test
 * [x] Double check formatting of docs examples

nodejs/examples/full_text_search.test.ts

@@ -0,0 +1,45 @@
+// SPDX-License-Identifier: Apache-2.0
+// SPDX-FileCopyrightText: Copyright The LanceDB Authors
+import { expect, test } from "@jest/globals";
+import * as lancedb from "@lancedb/lancedb";
+import { withTempDirectory } from "./util.ts";
+
+test("full text search", async () => {
+  await withTempDirectory(async (databaseDir) => {
+    const db = await lancedb.connect(databaseDir);
+
+    const words = [
+      "apple",
+      "banana",
+      "cherry",
+      "date",
+      "elderberry",
+      "fig",
+      "grape",
+    ];
+
+    const data = Array.from({ length: 10_000 }, (_, i) => ({
+      vector: Array(1536).fill(i),
+      id: i,
+      item: `item ${i}`,
+      strId: `${i}`,
+      doc: words[i % words.length],
+    }));
+
+    const tbl = await db.createTable("myVectors", data, { mode: "overwrite" });
+
+    await tbl.createIndex("doc", {
+      config: lancedb.Index.fts(),
+    });
+
+    // --8<-- [start:full_text_search]
+    const result = await tbl
+      .query()
+      .nearestToText("apple")
+      .select(["id", "doc"])
+      .limit(10)
+      .toArray();
+    expect(result.length).toBe(10);
+    // --8<-- [end:full_text_search]
+  });
+});