I'm still using the Monitoring (Classic) APIs currently. I've not found a "non-classic" version of the API, but I've also not spent much time looking. Since a web job runs as part of the Web App you'll need to monitor the web app using the tools provided in the Microsoft.WindowsAzure.Management.Monitoring.Metrics Namespace.
I found the API to be somewhat confusing, but spent sometime working with the PG to get it right. I've provided some sample code on the MSPFE github page at: https://github.com/mspfe/AzureMetricsAPISampleKit. Running the "tests" in this Solution will show you how to use the lib.
You first need to identify the web app by getting a list of them:
var webSpaceList = _webSiteClient.WebSpaces.List();
Then collect the availabile metrics:
foreach (var website in websiteList)
{
MetricDefinitionListResponse wsMetricListResponse = _metricsClient.MetricDefinitions.List(website.WebsiteResourceId, null, null);
website.MetricDefinitionsList = wsMetricListResponse.MetricDefinitionCollection;
website.MetricNamesList = new List();
foreach (var metric in website.MetricDefinitionsList.Value)
{
website.MetricNamesList.Add(metric.Name);
}
MetricValueListResponse wsValueResponse = _metricsClient.MetricValues.List(website.WebsiteResourceId, website.MetricNamesList, "",
_timeGrain, _startDateTime, _endDateTime);
website.MetricValueList = wsValueResponse.MetricValueSetCollection;
}
From there you should have metric definitions and values. Sorry if this code is a little dated... but it should work.