It certainly doesn't hurt to diversify your skills. If you really want to, take a step away from full featured engines to simpler frameworks, like LÖVE, prototype a bit with it and learn a new language in the process.
You can still use Unity in the end for all your "real" work, but I think learning more languages, frameworks and programming paradigms will help you improve your work in Unity, too as it gives you a bigger toolbox of ways to think about tackling certain problems.
It will also help your knowledge not to become obsolete should Unity ever fall out of favor of the dev community.
In my opinion, if you're a "real" programmer isn't determined by the tools you use but by the mindset you have. Always be curious, try new technologies and use the knowledge you gain from that in your daily work. I guess only ever applying knowledge you already have to new projects could become very boring after a while, too. Always push the limits of your knowledge, even if it's just to avoid being bored by your work.