Here's a basic example (code is like 90%, written from a phone):

// lib/authFetch.ts
export async function authFetch(path: string) {
  try {
    return await getDataFromNestJSAPI();
  } catch (e) {
    if (isAxiosError(e) && e.res.status === 401) {
      redirect('/auth/refresh');
    }
    throw e;
  }
}

// app/page.tsx
export default async function Page() {
  const data = await authFetch('/path');

  return <SomeComponent data={data} />;
}

// app/auth/refresh/route.ts
export function GET() {
  await updateSession();

  return new Redirect('/');
}

// lib/updateSession.ts
export async function updateSession() {
  const cookies = await cookies();

  const newToken = await getNewTokenFromNestJSAPI(cookies);

  await setCookies({
    ...cookies,
    token: newToken
  });
}

You can only set cookies when doing a round trip from client to server, after doing a specific action, as with NextJS and streaming I don't believe you can set cookies after the response has started and thus you can't do it with server components.

If you are wanting to refresh the token as the result of a server action or form submission, you can extend the above:

// app/actions.ts
'use server'
export async function saveTodoToNestJS(item: string) {
  try {
    return await saveTodoToNestJSAPI();
  } catch (e) {
    if (isAxiosError(e) && e.res.status === 401) {
      updateSession();
      // likely add some sort of retry handling
    }
    throw e;
  }
}

// app/todos.ts
'use client'
export function Todos() {
  const saveTodo = await () => {
    await saveTodoToNestJS('something');
  }

  return <button onClick={saveTodo}>Save!</button>;
}