Linked servers are, unfortunately, a very widely used practice. They're not a very widely recommended practice because of all the issues that they cause. However, they're so very convenient, making it so you don't have to move data around or duplicate it, that they get used all the time.

If you want to move to Platform as a Service SQL Database (as currently configured, changes are coming), you just have to unpick the threads of cross server queries. You have to assume no queries between servers (there is a way to do cross-database queries, but it's a little bit of work). Then do what's necessary. I'd suggest not picking a single approach for everything. In some cases, duplicating data will be better. In others, setting up a service so that the app can cross-connect data is a good choice.