feat: add web testing foundation with infra-backed suites (#349)

* feat: add web test framework with infra-backed suites

* fix: honor DATABASE_URL env in integration prepare script

* fix: apply web test review feedback

* fix: streamline web test infra lifecycle and workflow scope

apps/web/src/app/api/health/route.api.test.ts

@@ -0,0 +1,12 @@
+import { describe, expect, it } from "vitest";
+import { GET } from "~/app/api/health/route";
+
+describe("health route", () => {
+  it("returns healthy response", async () => {
+    const response = await GET();
+    const body = await response.json();
+
+    expect(response.status).toBe(200);
+    expect(body).toEqual({ data: "Healthy" });
+  });
+});