Does making the argument a generic parameter instead work for you?

So something like this:

abstract class BaseClass {
  public abstract userAuth<
    TResponse extends MyResponse = MyResponse,
    TError extends unknown = unknown
  >(): TResponse | UIError<TError>;
}

class TestClass extends BaseClass {
  public userAuth<
    TResponse extends MyResponse = MyResponse, TError extends unknown = unknown>(): TResponse | UIError<TError> {
      throw new Error("Method not implemented.")
  }
}