fix: make test suite runnable without DB/Chrome, add tests to CI

- Refactor index.ts to skip start() when NODE_ENV=test
- Add test setup with mocks for db, keys, browser, verification, email, usage
- Add vitest.config.ts with setup file
- Rewrite tests to work with mocks (42 tests, all passing)
- Add new tests: signup 410, recovery validation, CORS headers, error format, API root
- Add test step to CI pipeline before Docker build

vitest.config.ts

@@ -0,0 +1,9 @@
+import { defineConfig } from "vitest/config";
+
+export default defineConfig({
+  test: {
+    setupFiles: ["src/__tests__/setup.ts"],
+    testTimeout: 15000,
+    hookTimeout: 15000,
+  },
+});