Hello @Burch, Michael and welcome to Microsoft Q&A. Thank you for providing some high level background.
Solution patterns can be found in the Azure Architecture Center.
I would like to flush out your situation in a little more detail. Below is my understanding of your situation. This makes many assumptions, so please feel free to correct me.
You have a list of people, perhaps users of an application. Some are very active, some do not use it much, some have not used it in a long time.
Your appllication pushes notification of usage via Google Pub Sub. These notices contain among other things, the user's ID and the date/time of usage as it happens.
You want to consume the notices to update your list of users with the most recent date/time they used the application. With this information you can decide whether the use is active and should be kept, or is "retired" and should be "archived".
There are many Azure services. Whether there are any other Azure services you wish to integrate with can make a large difference.