Fluent builder pattern in TypeScript with type support

builder.ts

// Types Except & SetRequired from https://github.com/sindresorhus/type-fest
type Except<ObjectType, KeysType extends keyof ObjectType> = Pick<ObjectType, Exclude<keyof ObjectType, KeysType>>;

type SetRequired<BaseType, Keys extends keyof BaseType = keyof BaseType> = Except<BaseType, Keys> &
  Required<Pick<BaseType, Keys>> extends infer InferredType
  ? { [KeyType in keyof InferredType]: InferredType[KeyType] }
  : never;

class ChainableBuilder<T, X> {
  constructor(public args: T, public x: new (...args: any[]) => X) {}

  public set<K extends keyof T>(
    key: K,
    value: string,
  ): SetRequired<T, K> extends Required<T>
    ? ChainableBuilder<SetRequired<T, K>, X>
    : Omit<ChainableBuilder<SetRequired<T, K>, X>, "build"> {
    return new this.constructor({ ...this.args, [key]: value }, this.x);
  }

  public build(): X {
    return new this.x(this.args);
  }
}

class User {
  public email: string;
  private _password: string;

  constructor(args: Required<IUserBuilderOpts>) {
    this.email = args.email;
    this._password = args.password;
  }
}

interface IUserBuilderOpts {
  email?: string;
  password?: string;
}

const builder = new ChainableBuilder<IUserBuilderOpts, User>({}, User);
builder.set("email", "value").build(); // Property 'build' does not exist on type 'Pick<ChainableBuilder<{ password?: string | undefined; email: string; }, User>, "args" | "x" | "set">'.ts(2339)
builder.set("email", "value").set("email", "value").build(); // Property 'build' does not exist on type 'Pick<ChainableBuilder<{ password?: string | undefined; email: string; }, User>, "args" | "x" | "set">'.ts(2339)
builder.set("email", "value").set("password", "value").build(); // works
builder.build();