I'm trying to handle a basic prompt for password and login type application. I would like to set a cookie, then redirect the client to a new URL.

I am able to set the cookie, but I'm not able to get a redirect to work in any condition.

The form's submit function is below:

// /app/page.tsx
    async function onSubmit(event: FormEvent<HTMLFormElement>) {
        event.preventDefault()

        const formData = new FormData(event.currentTarget)

        const response = await fetch('/api/auth', {
            method: 'POST',
            body: formData
        })
        setSuccess(response.status);
    }

The following is the route handler for /app/api/auth. I am able to set a cookie in the two cases where I try it, but I am not able to execute a redirect at all.

// /app/api/auth/route.ts
export const runtime = 'edge';

import { NextRequest, NextResponse } from 'next/server'
import { redirect } from 'next/navigation';
import { useRouter } from 'next/navigation'

export async function POST(request: Request) {
    const data = await request.formData();

    // This doesn't redirect, but should
    // https://nextjs.org/docs/app/api-reference/functions/redirect
    console.log("do a redirect")
    redirect("/admin")
}

I've truncated this post to meet a message limit, but my tests with setting cookies are in the github repo https://github.com/timatlee/nextjs_redirect_testing. I can set cookies, but not able to redirect.