Are you open to working pretty much anywhere else? Yes.
Seriously, there's no doubt that Java and JEE aren't "cool" anymore, but there's also no question that a TON of companies still use Java, including JEE. There will most likely be jobs for people doing JEE for a long time to come.
That said, JEE is like anything else in terms of "don't put all of your eggs in one basket". From a career standpoint, it would probably be good to have some skills in something else as well, to hedge your bets a little. Python seems like a good choice, as it's widely used and has applications in many domains. That is, its uses range from web development, to "big data", to machine learning and data science, etc.
Or jump on the bandwagon for one of newer, uber-hip languages out there, to complement Java. Pick up Rust, or Go, or Julia or something.
There are a plethora of online learning resources, free and paid, that will teach you everything you need to know about the multitude of APIs.
Go to youtube, go to Lynda.com and go to Pluralsight.com, there you will find all the resources you need for free or very little cost to learn Java EE.