I'm trying to faithfully follow the next.js authentication guide to perform auth using a server action, which sets cookies using server side headers (as shown in the guide)

However, when I attempt to follow the steps, I'm met with an error about using server api in a client component, which I puzzling because it appears to be shown as correct by the docs

"You're importing a component that needs "server-only". That only works in a Server Component but one of its parents is marked with "use client", so it's a Client Component."

I've pushed up a POC example which started from create-next-app, and only added the relevant files from the authentication guide: https://github.com/bhurlow/nextjs-auth-example

I assume its possible to call a server action from a use client component like this: https://github.com/bhurlow/nextjs-auth-example/blob/main/app/ui/login-form.tsx#L7. Any suggestions?