Assuming that you have an Azure SQL Database, the answer is that you don't. Azure SQL is a PaaS service, and Microsoft are handling all the updates for you. The only means of control that you have is the compatibility level.
Yes, SELECT @@version returns something which looks seriously out of date. I don't know why they keep it that way.
The documentation for Azure SQL Database is the same for the normal SQL Server. On every page there is information to which flavours of SQL Server the topic applies to.
If you are in fact running SQL Server on an Azure VM, you do indeed to upgrade (or just tear down that VM and create a new). That is no different from upgrading on-prem.