The founding fathers of modern mountain bikes started with modified 1950s Schwinn cruisers in the hills of California. So yeah, they are up to the task.
https://en.wikipedia.org/wiki/Klunke...Mountain_Bikes
I say, keep doing what you are doing. As long as the bike fits you well and you are having fun, carry on. Over time your desires
may change. You might want a different fit, or riding position, or more speed, or suspension. My suggestion is, don't look for a "needed" change. Just ride, ride, ride, and and everything you need to know will make itself apparent to you through a natural process. Someday you may want to make some minor tweaks to your current bike, or you may discover that you'd like to try an entirely different angle. The miles will answer most of your questions.