Extract groombook/api from monorepo with CI workflow

- Add source code from apps/api
- Add packages/db and packages/types workspace dependencies
- Add GitHub Actions CI workflow (lint, typecheck, test, docker)
- Generate pnpm-lock.yaml
- Add .gitignore

Co-Authored-By: Paperclip <noreply@paperclip.ing>

src/__tests__/calendar.test.ts

@@ -0,0 +1,16 @@
+import { describe, it, expect } from "vitest";
+import { generateIcalToken } from "../routes/calendar.js";
+
+describe("generateIcalToken", () => {
+  it("generates a 64-character hex token", () => {
+    const token = generateIcalToken();
+    expect(token).toHaveLength(64);
+    expect(token).toMatch(/^[a-f0-9]+$/);
+  });
+
+  it("generates unique tokens", () => {
+    const token1 = generateIcalToken();
+    const token2 = generateIcalToken();
+    expect(token1).not.toBe(token2);
+  });
+});