Interesting. Some time ago I had the ongoing debate with a colleague on what it meant to be full stack.
I was under the impression that full stack meant you can do what's needed to stand up a solution at literally every OSI layer.
For example, from down at the base of infrastructure, networking, hardware/cloud, servers / platforms, integration, data / database, custom and COTs applications and services to clients, UI, desktop/web/thin/fat etc. etc.
By that measurement someone who can do all that probably already understands and in a sense, works in distributed systems - you probably had to already to cover the breadth and depth of all that knowledge.
Not picking on your choice of words here ("full stack"), just mulling it over and thinking: 1) if you can do that you're qualified to work on distributed systems and 2) there's no shortage of work advancing distributed systems and that problem isn't going away any time soon.
I'd say distributed systems is challenging (I worked on a startup doing that with database federation and it was really interesting and challenging), fun and important.
I think maybe the bigger question is, are you interested and want to dedicate the effort needed to get into it, and will that make you happy? There's so many levels of working in distributed systems - from research, inventing / building the tech, to implementing existing solutions (e.g. Apache Spark, Kubernetes etc. etc.).
If that stuff is interesting I'd first decide if I wanted to be on more on the research or practical side, and then how much money you need to live, and then choose my entry point into the field.
What does "backend" mean? Just the application layer? If you're writing a Tomcat application, do you have to know how to debug Tomcat itself and submit patches for issues? Do you need to know how to write a Java compiler or an OS kernel? Do you need to know how to design microprocessors? What about how to fab them?
Calling the top two layers of a very deep stack "full stack" is a bit strange.