cross-fetch: Types of property 'headers' are incompatible (with new 3.1.0)

(First of all thanks for this amazing package!)

We are using cross-fetch to use the same client calls to our APIs from other APIs and any running application. For our infrastructural needs, we created a small customFetch function on top of the fetch function so we could change the URL if a cloud parameter is passed or not:

export const customFetch = (input: RequestInfo, init: RequestInit, cloud?: CloudSubdomain | string): Promise<Response> => {
    let url = "";
    if (cloud) {
        url += createCloudUrl(cloud);
    }
    url += input;
    return fetch(url, init);
};

After updating to version 3.1.0 our code started to throw the following error:

Type 'Promise<import("/home/user/development/node_modules/cross-fetch/lib.fetch").Response>' is not assignable to type 'Promise<Response>'.
  Type 'import("/home/user/development/node_modules/cross-fetch/lib.fetch").Response' is not assignable to type 'Response'.
    Types of property 'headers' are incompatible.
      Type 'Headers' is missing the following properties from type 'Headers': [Symbol.iterator], entries, keys, values

22     return fetch(url, init);

I inspected the types from both node_modules/typescript/lib/lib.dom.d.ts and node_modules/cross-fetch/lib.fetch.d.ts and I see no difference apart from this:

declare var Headers: {
    prototype: Headers;
    new(init?: HeadersInit): Headers;
};

Hope you can shed some light on this. Thanks for your time!