Be careful about applying for internships. Many of them stipulate that the intern must be a current student for the entire length of the internship and they are not for recent graduates. These internships are explicitly a hiring funnel to try and get the brightest students to commit early to the company where they had their internship. If you're going to have already graduated by the time the internship would happen, it simply isn't relevant to you in most companies.
Cram leetcode (aka interview skills) and keep applying to large companies through their websites. Your university's job board will help mostly with finding local companies near the university, but they are not the sum total of your opportunities, not by far. Furthermore, companies that post on university job boards get flooded with applications from that school, so they'll stick with the school's cream of the crop. Start with FAANG and then work your way down the Fortune 500. Small companies / startups need people with established track records because they need to produce results quickly; large companies have built the internal processes over time that protect the company from the inexperience of junior engineers and will therefore prefer to hire junior engineers in order to save money.
The industry is in dire need of labor so it shouldn't really matter what you put on your resume, as long as you put down that you have a CS degree and you're applying for junior engineering positions at large-enough companies, quite frankly that should be enough to at least get you a phone call for initial HR screening. If you're not progressing to other interviews or offers, that's a different question, and barring any personality complications that could come up ("interview skills") it probably goes back to you needing to cram leetcode ("technical skills").
If your resume isn't getting you phone calls, find someone in your career center and ask them to help you with your résumé. You don't need it to stand out - not in this jobs climate. You just need to make sure you're not making stupid mistakes with it.