If your uni has one, make use of their employment advice and job placement services, because they may not offer them to alumni. You can get some advice on writing CVs, cover letters and job hunting.

If you don't have work experience and/or are looking for further study in academia, try to make time to go back and thank all the professors you had a good relationship with (and even ones you didn't) in whatever field you may want to continue study in. Sound out whether they would be willing to be a reference when you apply for future jobs/programs. You'll get a much better (and timely) response if you ask now than if you ask in six months'/one/two years' time.

If your uni has a subsidised medical clinic, pay them a visit if you need/want a checkup. GPs outside of uni can be pretty dismissive of younger people's illnesses and concerns.

Check when the cutoff is for your access to things like the library/online journals/jobs board/bulletin board/student discounts. Make the most of these while you're on them.

I know you say in your post putting relationships with your classmates aside, and this is kinda related but, if there are clubs or societies related to your interests you could consider joining them. It's never too late (I know most clubs get their big numbers boost from first-years, but there are post-grad/professional affiliation clubs too for people in later years of their study). I joined a club that had a presence beyond just the uni chapter, and that meant I was able to stay involved/network (dreaded term) while job hunting.

Sorry for the like, job-focussed practical stuff, it is a pretty big step and losing access to a lot of those social platforms and services that uni offers can be jarring