feat(api): standardize errors as problem details

apps/web/src/lib/problem-response.test.ts

@@ -0,0 +1,29 @@
+import { describe, expect, it } from "vitest";
+import { problemInstance, problemResponse } from "./problem-response";
+
+describe("problemResponse", () => {
+  it("uses the request path and query as the problem instance", () => {
+    expect(problemInstance(new Request("https://example.com/api/items?cursor=next")))
+      .toBe("/api/items?cursor=next");
+  });
+
+  it("returns RFC 9457 JSON with the required media type", async () => {
+    const response = problemResponse({
+      type: "urn:error:unauthorized",
+      title: "Unauthorized",
+      status: 401,
+      detail: "A valid Velocity server credential is required.",
+      instance: "/api/velocity/access",
+    });
+
+    expect(response.status).toBe(401);
+    expect(response.headers.get("content-type")).toBe("application/problem+json");
+    expect(await response.json()).toEqual({
+      type: "urn:error:unauthorized",
+      title: "Unauthorized",
+      status: 401,
+      detail: "A valid Velocity server credential is required.",
+      instance: "/api/velocity/access",
+    });
+  });
+});