I've tried

import { NextRequest as OriginalNextRequest } from "next/server";

declare global {
    declare interface NextRequest extends OriginalNextRequest {
        auth: any
    }
}

and made sure I'm not importing NextRequest from next/server (as to not override the new declaration) and I'm getting the following error:

Type '(next: NextMiddleware) => (request: NextRequest, _next: NextFetchEvent) => Promise<NextMiddlewareResult>' is not assignable to type 'MiddlewareFactory'.
  Type '(request: NextRequest, _next: NextFetchEvent) => Promise<NextMiddlewareResult>' is not assignable to type 'NextMiddleware'.
    Types of parameters 'request' and 'request' are incompatible.
      Property 'auth' is missing in type 'import("p:/cts-final/frontend/node_modules/next/dist/server/web/spec-extension/request").NextRequest' but required in type 'NextRequest'.