NestJS + mongoose: how to find and set sub document values by object or array

sub-documents-in-array.ts

export class MyModel extends BaseModel {
  @prop({ required: false, items: MyModel })
  items: MyModel[];
}

export class ModelService extends BaseService {
  async findByNestedField(key: string): Promise<MyModel> {
    return await this.findOneAsync(
      {
        items: {
          $elemMatch: { key: key }
        }
      }
    );
  }
    
  async setNestedField(id: string, key: string, nestedFieldValue: any): Promise<void> {
    // TODO: this does not work!!
    await this.model.updateOne(
      {
        _id: id,
        items: {
          $elemMatch: {
            key: key,
          },
        },
      },
      {
        $set: {
          'items.$.nestedField': nestedFieldValue
        },
      },
    );
  }
}

sub-documents-in-object.ts

export class MyModel extends BaseModel {
  @prop({ required: false, items: MyModel })
  items: Record<string, MyModel>;
}

export class ModelService extends BaseService {
  async findByNestedField(key: string): Promise<MyModel> {
    return await this.findOneAsync(
      {
        [`items.${key}`]: {
          $exists: true,
        },
      }
    );
  }
    
  async setNestedField(id: string, key: string, nestedFieldValue: any): Promise<void> {
    const putObject = {};
    putObject['items.' + key] = {
      key: key,
      nestedField: nestedFieldValue,
    };
    return await this.model
      .findByIdAndUpdate(id, { $set: putObject })
  }
}