NextJS rewrite does not delete URL search param

I have an email auth and after user clicks the button to access my website I have to check whether they have tokens or not. When they are redirected to my page from Gmail they have verification_token=** searchParam and if they have already been authorized I have to delete it.

As NextJS docs say, I have to use NextResponse.rewrite function in middleware.ts with deleting that token but next just shows the page with the same search param. I use app router and Next 14

As I mentioned, I used rewrite function with deleting the searchParam with url.searchParams.delete('verification_token'); but it does not help. The param is still there.

I have tried multiple variants with nextResponse.redirect etc. but nothing helped.

The NextResponse.rewrite function proxies requests, so the url shouldn't change. Using NextResponse.redirect worked for me:

import { NextResponse } from "next/server";

export function middleware(req) {
  const nextUrl = req.nextUrl;

  if (nextUrl.searchParams.has("verification_token")) {
    nextUrl.searchParams.delete("verification_token");
    return NextResponse.redirect(nextUrl);
  } else {
    return NextResponse.next();
  }
}