How to use OMS for Azure web app
I think it's too late but here it goes, Application insight is what you will need to get the metrics, Have you looked at it as an option?
OMS, is more useful when you are running stuff on Infrastructure as service resources not on Paas/Saas, I guess because the shared responsibility monitoring etc is different in such environment & PaaS/SaaS should already have means to log, monitor & alert.
Though there is workaround to integrate your app for logging that I am aware of, All you need to do integrate the log analytics for your app service, from there you can setup alerting etc.
Installing agent on shared service would never work out, considering there will be other neighbors using the resources however dedicated instances of app will give you greater flexibility.
Thanks