Can I update my Microsoft Enterprise SQL Server?
Given that you work for a company that is using Enterprise Edition I'm going to assume you aren't touching one of their servers.  If you are please don't. As mentioned in the comments this could be a very expensive mistake and if the work you are doing is on any company asset please contact the company's DBA. That's what they are there for.

That said, let me explain a few things.


SQL Server Management Studio is an interface used to connect to the SQL Server Database Engine (among other things).  It's version is completely separate these days from the database engine.  So you could very easily be on SSMS 18 while working with SQL Server 2008.
While some functionality is actually part of the GUI things like STRING_AGG are actually functions of the language T-SQL that is not part of the GUI and requires you update the database engine.


It looks like you got this far on your own but I just wanted to be sure.  

Now, if you are trying to set yourself up a home lab, or are you a company workstation and have permission to install a single user development version of SQL Server then it's perfectly reasonable to want to upgrade SQL to try out new functionality. In this case you'll want the Developer Edition of SQL Server.  It's a free single user license that can only be used for development/experimentation. It's also has the same functionality as the Enterprise version of SQL Server so you'll have everything you want.

You can get it here: https://www.microsoft.com/en-us/sql-server/sql-server-downloads

If your home machine/workstation has the resources I would recommend installing more than one version of SQL on it. The version you are working on at work, and the latest edition that you want to play with.

Last thing, if you are working on a shared environment you really need to contact your DBA and make sure that nothing has been broken. Upgrading SQL can have implications on existing functionality and could potentially break an existing application.