feat: implement error handling and validation middleware, enhance result handling

Co-authored-by: Copilot <copilot@github.com>

apps/backend/src/lib/http/handle-result.ts

@@ -0,0 +1,20 @@
+import type { Context } from 'hono'
+import type { ContentfulStatusCode } from 'hono/utils/http-status'
+import type { Result } from '@/lib/result'
+import { mapAppErrorToProblem } from './problem-mapper'
+
+export function handleResult<T>(
+  c: Context,
+  result: Result<T>,
+  successStatus: ContentfulStatusCode = 200
+) {
+  if (!result.ok) {
+    const requestId = c.get('requestId') as string | undefined
+    const instance = requestId ? `/requests/${requestId}` : undefined
+    const problem = mapAppErrorToProblem(result.error, instance)
+
+    return c.json(problem, problem.status)
+  }
+
+  return c.json(result.value, successStatus)
+}