feat(web): minimal shared-password auth gate

The web app had no auth — anyone reaching the host could browse the library,
trigger downloads, and read/overwrite the stored credentials in Settings. Adds
an opt-in single-shared-password gate:

- Next.js middleware redirects unauthenticated page requests to /login and
  returns 401 for /api/*; static assets are excluded via matcher.
- Auth is enabled ONLY when LYRA_PASSWORD is set (unset ⇒ app stays open, so
  existing deployments are unchanged). Documented in README "Security".
- The session cookie is httpOnly and carries HMAC-SHA256(password) keyed by
  LYRA_SECRET_KEY — unforgeable, and the plaintext password never touches the
  client. Edge-safe Web Crypto so one lib/auth.ts serves middleware + route.
- Cookie is NOT Secure: Lyra serves plain HTTP on the LAN; a Secure cookie would
  loop. Works behind an HTTPS proxy too.
- /login page + form, a Sign out button (shown only when auth is enabled), and
  chrome (nav + worker-status poll) suppressed on /login.
- docker-compose passes LYRA_PASSWORD to web; .env.example documents it.

Verified live end-to-end (built + next start): no-cookie page→307 /login,
API→401, wrong password→401, correct→200+cookie, authed page/API→200, forged
cookie→401, and the auth-disabled (no LYRA_PASSWORD) path stays fully open.
web 133 tests green, tsc clean.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

web/src/lib/auth.test.ts

@@ -0,0 +1,40 @@
+import { describe, it, expect, beforeEach } from "vitest";
+import { expectedToken, safeEqual } from "./auth";
+
+beforeEach(() => {
+  process.env.LYRA_SECRET_KEY = "MDEyMzQ1Njc4OWFiY2RlZjAxMjM0NTY3ODlhYmNkZWY=";
+  delete process.env.LYRA_PASSWORD;
+});
+
+describe("auth token", () => {
+  it("returns '' when no password is configured (auth disabled)", async () => {
+    expect(await expectedToken()).toBe("");
+  });
+
+  it("derives a stable, non-empty token from the password", async () => {
+    process.env.LYRA_PASSWORD = "hunter2";
+    const a = await expectedToken();
+    const b = await expectedToken();
+    expect(a).not.toBe("");
+    expect(a).toBe(b); // deterministic
+  });
+
+  it("changes with the password and with the secret key", async () => {
+    process.env.LYRA_PASSWORD = "hunter2";
+    const base = await expectedToken();
+    process.env.LYRA_PASSWORD = "different";
+    expect(await expectedToken()).not.toBe(base);
+    process.env.LYRA_PASSWORD = "hunter2";
+    process.env.LYRA_SECRET_KEY = "ZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmY=";
+    expect(await expectedToken()).not.toBe(base);
+  });
+});
+
+describe("safeEqual", () => {
+  it("matches equal strings and rejects others", () => {
+    expect(safeEqual("abc", "abc")).toBe(true);
+    expect(safeEqual("abc", "abd")).toBe(false);
+    expect(safeEqual("abc", "ab")).toBe(false);
+    expect(safeEqual("", "")).toBe(true);
+  });
+});