Run and await a coroutine as a task

I'm trying to move away from unity's coroutines and callbacks in favor of async/await.

I have the following code using coroutines:

public IEnumerator GetProfileJson(string address, GetProfileSuccess onSuccess, GetProfileFailed onFail)
{
    var queryRequest = new QueryUnityRequest<GetDataFunction, GetDataOutputDTO>(RpcUrl, null);
    yield return queryRequest.Query(new GetDataFunction(), address);
    if(queryRequest.Result == null)
    {
        onFail?.Invoke(new NullResponseException());
        yield break;
    }

    byte[] resultBytes = queryRequest.Result.Values[0]; 
    string url = Encoding.UTF8.GetString(resultBytes);

    using WebClient web = new WebClient();  
    string json = web.DownloadString(url);

    onSuccess?.Invoke(json);
}

I would like to convert it to something like this:

public async Task<string> GetProfileJson(string address)
{
    var queryRequest = new QueryUnityRequest<GetDataFunction, GetDataOutputDTO>(RpcUrl, null);
    
    await Task.Run(() => // Somehow await this coroutine's completion
    {           
        queryRequest.Query(new GetDataFunction(), address);
    });
    
    if(queryRequest.Result == null)
    {
        throw new NullResponseException();
        yield break;
    }
    
    byte[] resultBytes = queryRequest.Result.Values[0]; 
    string url = Encoding.UTF8.GetString(resultBytes);
    
    using WebClient web = new WebClient();  
    string json = await web.DownloadStringTaskAsync(url);
    
    return json;
}

But I just can't figure out how to run and await this line queryRequest.Query(new GetDataFunction(), address);

The Query method is from Neuthereum's API and looks like this

public IEnumerator Query(string contractAddress, BlockParameter blockParameter = null)
{
    yield return Query(new TFunctionMessage(), contractAddress, blockParameter);
}