Right at the moment you really have choices on which way you want to go. And you aren't locked into either side.

There are two types of DBA's (without getting into the weeds).

There is the production DBA who knows how to setup a SQL Server from scratch, install vendor apps, troubleshoot slowness and maybe some troubleshooting the apps and why they aren't working at the moment. They might also be able to troubleshoot networking issues and the server or even do an install of the server.

Then there are the development (and subtype QA) DBAs that build the stored procedures, functions, DBs and the rest.

Going either way is up to you.

My prior job was doing a lot of programming in VBA with Access front-ends for about five years. Then I went to pure production DBA with both Oracle and SQL along with the network/server work.

My current job that I was hired for was the production DBA with over a hundred hosted SQL Servers and in-depth front-line troubleshooting of my company's software.

There is nothing stopping you from going either, or both ways, over the course of your career. There is no lock, but your course of study and decisions make a difference. My suggestion is that you never turn down any opportunity to learn.

My portfolio and resume has references to SQL Server Central, Experts Exchange and other sites. Those are publicly visible and aren't dependent on your current employer.

If you can answer questions in any of those, that shows an interviewer that you know stuff and are trying to learn.