From my experience, the best way to convey yourself through your resume when it comes to internships is to show as much as you can about yourself and character, as well as your experience & accomplishments. Try to squeeze all that you can onto a 1-pager, no tech internship resume should be longer than 1 page. (If Elon Musk can do it, so can you https://novoresume.com/career-blog/elon-musk-one-page-resume)
Have a small "Profile" of you, which can just be a 2 or 3 sentence blurb about what you want to gain from this internship & why you're the right fit. List experiences, skills, accomplishments, as well as your interests, passions, and any other insights that show more about who you are besides the person with X,Y,Z skills with Java or Python.
If you want to include past projects or a portfolio, make sure to have your Github page on your resume, or even a link to a personal website to show more information if they need.
Good luck on the application, I know the process is stressful and long. All the best!