You have to use useSearchParams in the Movies component to read the query string in the URL:

1. The Routes:

<Routes>
  <Route path="/" element={<Layout />}>
    <Route index element={<Search />} />
    <Route path="search" element={<Movies />} />
  </Route>
</Routes>

2. the Movies component:

import { Navigate, useSearchParams } from "react-router-dom";


function Movies(props) {

  const [searchParams, setSearchParams] = useSearchParams();

  const page = searchParams.get("page");
  const otherParam = searchParams.get("otherParam");

  if(!page && !otherParam) {
    return <Navigate to="/" replace />
  }

  // the rest of your component
  ...

}

Or using URLSearchParams.keys()

import { Navigate, useSearchParams } from "react-router-dom";

function Movies() {
  const [searchParams, setSearchParams] = useSearchParams();

  if (![...searchParams.keys()].length) {
    return <Navigate to="/" replace />;
  }

  return <span>Movies page</span>;
}

react-router-dom and the Route component doesn't use or reference the URL queryString when matching routes. This is something the routed component should check or something you can create a special layout route component to handle. The code should use the useSearchParams hook to access the searchParams and check for the existence of any params.

Example:

This example is a layout route that checks the search params entries array length and if there are entries an Outlet component is rendered for any nested Route components to render their element prop out on, otherwise a redirect back to "/" is rendered.

import { Navigate, Outlet, useSearchParams } from 'react-router-dom';

const ParamsRoute = () => {
  const [searchParams] = useSearchParams();
  
  return searchParams.entries().length
    ? <Outlet />
    : <Navigate to="/" replace />
};

Usage:

<Routes>
  <Route path="/" element={<Layout />}>
    <Route index element={<Search />} />
      <Route element={<ParamsRoute />}>
        <Route path="search" element={<Movies />} />
      </Route>
  </Route>
</Routes>

Perhaps you want specific queryString parameters to be present:

import { Navigate, Outlet, useSearchParams } from 'react-router-dom';

const ParamsRoute = ({ params = [] }) => {
  const [searchParams] = useSearchParams();
  
  return searchParams.entries().length                // has params
    && params.every(param => searchParams.get(param)) // has required params
      ? <Outlet />
      : <Navigate to="/" replace />
};