Next.js, how to submit a form to another page?

I ended up catching the submit event and pushing a URL onto the router.

import {useState} from 'react'
import {useRouter} from 'next/router'

const preventDefault = f => e => {
  e.preventDefault()
  f(e)
}

export default ({action = '/search'}) => {
   const router = useRouter()
   const [query, setQuery] = useState('')

   const handleParam = setValue => e => setValue(e.target.value)

   const handleSubmit = preventDefault(() => {
     router.push({
       pathname: action,
       query: {q: query},
     })
   })

   return (
     <form onSubmit={handleSubmit}>
       <input
         type='text'
         name='q'
         value={query}
         onChange={handleParam(setQuery)}
         placeholder='Search'
         aria-label='Search'
       />
     </form>
   )
}

Based on the Next.js' routing system and Router API:

The Next.js router allows you to do client-side route transitions between pages, similarly to a single-page application. A special React component called Link is provided to do this client-side route transition.

Router.push also handles client-side transitions, and this method is useful for cases where next/link is not enough.

So it seems that you can only perform client-side transitions by using any of those two ways.

Using the form above will trigger a behavior as described by MDN docs for a form submission, as none of the above rules applies:

...The server then responds, generally handling the data and loading the URL defined by the action attribute, causing a new page load (or a refresh of the existing page, if the action points to the same page).

I also found another reference close to your question in Next.js' issues board, where the preferred method to follow, was the one you've also described as a solution.