I had the same issue where my API worked locally but returned 405 Method Not Allowed after deploying to Vercel.

For me, the problem was Vercel Authentication (https://vercel.com/docs/security/deployment-protection) blocking unauthenticated requests.

Fix: Go to your project in Vercel Dashboard. Navigate to Settings → General. Disable "Vercel Authentication". After disabling this setting, my API started working again!