How to refresh Laravel cookie with vue?

I have some routes in Laravel for which I have middleware setup for simple cookie authentication. I basically ask for a password and if they enter the correct password, I set a cookie which allows them to view the page.

Unauthed flow

User goes to URL -> password page -> user lands at desired page

Authed flow

User goes to URL -> user lands at desired page

Here is my code

Controller

public function gate_check(Request $request)
{
  $stored_password = Page::where('url', session('page'))->first()->password;
  $password = $request->password;

  if($password === $stored_password){
    Cookie::queue(cookie::make(session('page'), 'true', 20));
    return redirect()->route('upload', session('page'));
  } else {
    return back();
  }
}

Middleware

public function handle($request, Closure $next)
{
   if(Cookie::get($request->route('url'))){
     return $next($request);
   }
   session(['page' => $request->route('url')]);
   return redirect()->route('gate');
}

You may notice in the controller method that I set the cookie expiry to 20 minutes on this line Cookie::queue(cookie::make(session('page'), 'true', 20));

The pages the users go to are single page vue applications that perform file uploads via ajax.

The problem

If a user spends longer than 20mins on the page, the cookie expires and any upload requests fail due to a CSRF mismatch (a page refresh is needed in order to trigger the auth flow to get a fresh cookie)

But doing a page refresh could potentially waste a lot of time for the user as it will void anything they've done in the page prematurely.

The question

How can I, with JS, extend/prolong/refresh the cookie from Laravel? Essentially I need a popup asking them to re-enter the password again... (which avoids a page refresh) which I know how to do except for the actual refreshing/setting of the cookie part.