feat(web): useSearch infinite query + useDebouncedValue + MSW search handler

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

web/src/lib/use-debounced-value.test.tsx

@@ -0,0 +1,24 @@
+import { useState } from "react";
+import { expect, test } from "vitest";
+import { screen } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import { renderApp } from "../test/render";
+import { useDebouncedValue } from "./use-debounced-value";
+
+function Harness() {
+  const [text, setText] = useState("");
+  const debounced = useDebouncedValue(text, 150);
+  return (
+    <div>
+      <input aria-label="in" value={text} onChange={(e) => setText(e.target.value)} />
+      <span data-testid="out">{debounced}</span>
+    </div>
+  );
+}
+
+test("reflects the value after the delay", async () => {
+  renderApp(<Harness />);
+  await userEvent.type(screen.getByLabelText("in"), "bronze");
+  await screen.findByText("bronze");
+  expect(screen.getByTestId("out")).toHaveTextContent("bronze");
+});