test(http,immich): prove User-Agent fix at the wire level

Add two regression tests that fail on v1.76.0 and pass with the fix:
- wire-level test: a Headers instance (the shape @immich/sdk hands over)
  must reach the remote server with all headers intact
- real-SDK e2e: getServerStatistics through fetchWithTrustedCertificatesAsync
  against a live local server must deliver x-api-key

packages/integrations/test/immich-sdk-e2e.spec.ts

@@ -0,0 +1,37 @@
+// @vitest-environment node
+
+import { createServer } from "node:http";
+import type { AddressInfo } from "node:net";
+
+import { getServerStatistics, init } from "@immich/sdk";
+import { describe, expect, test, vi } from "vitest";
+
+import { fetchWithTrustedCertificatesAsync } from "@homarr/core/infrastructure/http";
+
+vi.mock("@homarr/core/infrastructure/certificates", () => ({
+  getAllTrustedCertificatesAsync: vi.fn(async () => []),
+  getTrustedCertificateHostnamesAsync: vi.fn(async () => []),
+}));
+
+describe("real @immich/sdk end-to-end through fetchWithTrustedCertificatesAsync", () => {
+  test("x-api-key set via init() reaches the server", async () => {
+    let receivedXApiKey: string | string[] | undefined;
+    const server = createServer((req, res) => {
+      receivedXApiKey = req.headers["x-api-key"];
+      res.writeHead(200, { "Content-Type": "application/json" });
+      res.end(JSON.stringify({ usage: 1000, photos: 5, videos: 2 }));
+    });
+    await new Promise<void>((resolve) => server.listen(0, resolve));
+    const port = (server.address() as AddressInfo).port;
+
+    init({ baseUrl: `http://127.0.0.1:${port}/api`, apiKey: "sdk-configured-key" });
+    const stats = await getServerStatistics({
+      fetch: fetchWithTrustedCertificatesAsync as unknown as typeof fetch,
+    });
+
+    server.close();
+
+    expect(receivedXApiKey).toBe("sdk-configured-key");
+    expect(stats).toMatchObject({ usage: 1000, photos: 5, videos: 2 });
+  });
+});