SQL Server 2016, Invalid object name 'STRING_SPLIT'

Make sure that the database compatibility level is 130

you can use the following query to change it:

ALTER DATABASE [DatabaseName] SET COMPATIBILITY_LEVEL = 130

As mentioned in the comments, you can check the current compatibility level of a database using the following command:

SELECT compatibility_level FROM sys.databases WHERE name = 'Your-Database-Name';

I was using Split_string, which felt grammatically correct in English, but my old eyes didn't see that it should be STRING_SPLIT ... so, if you're a bit mentally challenged like me, then check you've typed the command the right way! :)

If you can't change the COMPATIBILITY_LEVEL of the database you are working in, you can try looking at other databases on the same server to find one with a higher COMPATIBILITY_LEVEL. I found that the "master" database on my target server was at COMPATIBILITY_LEVEL = 140, so I connected to that database, and then executed my query, which actually ran against (fully qualified) tables in other databases on the server whose COMPATIBILITY_LEVEL was less than 130. It worked! Just query the various databases on your server with

SELECT compatibility_level  FROM sys.databases WHERE name = '<database_name>'; 

to find one that is >= 130.