feat(search): server-side offset pagination through providers + /search route (#115 backend)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/music/bilibili.test.ts

@@ -0,0 +1,39 @@
+import { describe, it, expect, vi } from "vitest";
+import { BiliBiliProvider } from "./bilibili.js";
+
+describe("BiliBiliProvider.search pagination", () => {
+  function mockProvider() {
+    const p = new BiliBiliProvider();
+    const get = vi.fn().mockResolvedValue({ data: { data: { result: [] } } });
+    // Short-circuit the buvid + wbi bootstrap so search only issues the
+    // /search/type request we want to inspect.
+    (p as any).buvidInitialized = true;
+    (p as any).wbiMixinKey = "0".repeat(32);
+    (p as any).wbiKeyFetchedAt = Date.now();
+    (p as any).api = { get };
+    return { p, get };
+  }
+
+  function searchParams(get: ReturnType<typeof vi.fn>) {
+    const call = get.mock.calls.find(
+      (c: any[]) => c[0] === "/x/web-interface/wbi/search/type"
+    );
+    expect(call, "expected a /search/type call").toBeTruthy();
+    // signWbi stringifies every value.
+    return call![1].params as Record<string, string>;
+  }
+
+  it("adds page (offset/limit+1) alongside page_size", async () => {
+    const { p, get } = mockProvider();
+    await p.search("hello", 20, 20); // page 2
+    const params = searchParams(get);
+    expect(params.page).toBe("2");
+    expect(params.page_size).toBe("20");
+  });
+
+  it("defaults offset to 0 → page 1 (backward compatible)", async () => {
+    const { p, get } = mockProvider();
+    await p.search("hello", 20);
+    expect(searchParams(get).page).toBe("1");
+  });
+});