Learn from the best engineers and pick up as many skills from them as possible
Become a founder
Given that, should I work on side projects full-time and apply to incubators or continue doing internships like my current one and doing side projects on the side?
These 2 goals kind of conflict as it will be tricky to learn from others, especially in the more mentor <-> mentee kind of way, as a founder. You will be learning on your own, on the fly.
I personally think hybridizing is the way to go. The side projects help build the skills necessary to start your own thing, and the internships help you get full-time employment and income.
Unless you're some kind of coding prodigy with some massive side projects already launched, I think it's best to get at least 2-3 years in the industry before pushing to become a founder. Being a good founder requires a lot of skills in general, with being able to collaborate/communicate well with others at around the top of that list.