fix(server): attach raw Error to res.err and avoid pino err key collision

Extract attachErrorContext helper to DRY up the error handler, attach the
original Error object to res.err so pino can serialize stack traces, and
rename the log context key from err to errorContext so it doesn't clash
with pino's built-in err serializer.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/__tests__/error-handler.test.ts

@@ -0,0 +1,53 @@
+import type { NextFunction, Request, Response } from "express";
+import { describe, expect, it, vi } from "vitest";
+import { HttpError } from "../errors.js";
+import { errorHandler } from "../middleware/error-handler.js";
+
+function makeReq(): Request {
+  return {
+    method: "GET",
+    originalUrl: "/api/test",
+    body: { a: 1 },
+    params: { id: "123" },
+    query: { q: "x" },
+  } as unknown as Request;
+}
+
+function makeRes(): Response {
+  const res = {
+    status: vi.fn(),
+    json: vi.fn(),
+  } as unknown as Response;
+  (res.status as unknown as ReturnType<typeof vi.fn>).mockReturnValue(res);
+  return res;
+}
+
+describe("errorHandler", () => {
+  it("attaches the original Error to res.err for 500s", () => {
+    const req = makeReq();
+    const res = makeRes() as any;
+    const next = vi.fn() as unknown as NextFunction;
+    const err = new Error("boom");
+
+    errorHandler(err, req, res, next);
+
+    expect(res.status).toHaveBeenCalledWith(500);
+    expect(res.json).toHaveBeenCalledWith({ error: "Internal server error" });
+    expect(res.err).toBe(err);
+    expect(res.__errorContext?.error?.message).toBe("boom");
+  });
+
+  it("attaches HttpError instances for 500 responses", () => {
+    const req = makeReq();
+    const res = makeRes() as any;
+    const next = vi.fn() as unknown as NextFunction;
+    const err = new HttpError(500, "db exploded");
+
+    errorHandler(err, req, res, next);
+
+    expect(res.status).toHaveBeenCalledWith(500);
+    expect(res.json).toHaveBeenCalledWith({ error: "db exploded" });
+    expect(res.err).toBe(err);
+    expect(res.__errorContext?.error?.message).toBe("db exploded");
+  });
+});