test(web-app): add cypress for unit test

web-app/cypress.config.ts

@@ -0,0 +1,27 @@
+import { defineConfig } from "cypress";
+
+export default defineConfig({
+  e2e: {
+    specPattern: "tests/e2e/*.spec.ts",
+    baseUrl: "http://localhost:8080",
+    supportFile: "tests/support/e2e.ts",
+    setupNodeEvents(on, config) {
+      on("before:browser:launch", (browser, launchOptions) => {
+        // Allow tests to run even if baseUrl is not available
+        // This is useful for unit tests that don't need a server
+        if (process.env.CYPRESS_SKIP_SERVER_CHECK === "true") {
+          config.baseUrl = null;
+          return config;
+        }
+        return launchOptions;
+      });
+    },
+  },
+  component: {
+    devServer: {
+      framework: "vue",
+      bundler: "webpack",
+    },
+    specPattern: "src/**/*.cy.ts",
+  },
+});