Try to shift some of your focus to things you can make and get small achievements in. For example, getting more fit and working out. Your initial goal isn't going to be about being better than a friend or "the average" or even what you might remember from when you were younger. Spend a couple of days benchmarking yourself, even if you feel like really lethargic, imagine the bare minimum and make a little less than that your expectations. When I was going through a rough time, going outside and going to a gym was an achievement. Even if all I did was go there, go in the gym and pretend to do some stretches and then leave again, that was still more than I did the day before. Do that for a week and you might start to think, since you're going to the gym and spending time there, might as well do some activities. This isn't about getting fit, until you want to make that step, it's about moving.

I'll give you a breakdown of my initial fitness ladder, each step a few days or a week.
Go to the gym for 10 minutes and stare at the tv and leave. Go to the gym for 20 minutes, find a tv I like and do some stretches near it, and then leave. Go to the gym and chill on the elliptical for 15 and leave. Go to the gym and try running and get tired after 5 minutes so I do another 5 minutes on an elliptical and leave. Go at a less busy time so I can try out different machine and see where I stand with each weight for 20 minutes. Find that there's a basketball court and borrow a ball from the front desk and shoot a few hoops for 15. Workout for 10 minutes and then stretch for 20.

I know it sounds weird that I am recommending the gym when you said you feel lethargic, but I promise any kind of workout is energizing. In fact just being near people that I can see are pushing themselves encourage me to try a bit harder too, even on days I didn't feel like it.

It's a good environment, and I know it might seem a little intimidating, but I promise no matter what day you go, you're not going to be the only person going for the first time. If nature and outdoors is your thing, that's cool, but for me the social aspect of it is important. I rarely talked to anyone other than the front desk person. It didn't matter, it was just about being around people and not alone. People that judge you for your performance at a gym are going to the gym for the wrong reason. All that matters is you do a little better on the long term average. If you feel weird or concerned about anything, ask the staff. Most places they are pretty bored and they'll want to help you, especially if you're new. They don't want to see you get hurt and that's the perspective you should keep.

Everyone starts somewhere

And over time I've worked up to being able to do an hour in the gym without thinking about it and I fell back in love with biking which I used to do as a kid. I love badminton and it was fun finding people to play with. I got into archery as well. I loved group fitness activities, not zumba, but Yoga was critical to my recovery. It wasn't that Yoga class is anything special, it was that teachers of yoga always approach it from a place of healing or restorative vibes. If the teacher is pretentious or makes you feel bad about not being able to do something, they're a bad teacher and you shouldn't continue their class.

If you want to feel confident about your first day, if you want to prepare, there's tons of yoga instructional videos on youtube for free. If you'd rather do things alone, that's fine too. I would just strongly recommend you reconsider and try it out in a group setting.

The reason why I focused on fitness is because it's something I genuinely didn't care about growing up. That meant I had no expectations for myself. Even the smallest achievements were meaningful and that feeling helped me pull myself out of that rut.

I would explore if there's some underlying mental or physical health concern if the lethargy is seriously becoming a detriment to your everyday function. Generally, for students, there's a mental healthcare provider you can access for free. It doesn't have to be therapy or even an ongoing thing, it could just be a visit to sit and talk to someone for an hour and have them help you figure out what's going on. Taking care of yourself means getting yourself checked out by a professional. They get paid to help you out. If you are feeling sick and it's not really getting better, you go to a doctor and they tell you if it'll go away on its own or if there's something more to be worried about. The same is true for mental health, but not everyone see it without stigma. It's your body and life, you don't need to care about what other people will think about it.

If you're in a place where access to professional is limited, there's a youtube channel I recommend Dr K. He's a Psychiatrist who did his residency at Harvard. He talks to online to popular streamers and gamers and his open discussions helped some of my friends change their perspective on what addressing mental health concerns means.

3 Motivation Styles determined by Personality by Dr. K https://www.youtube.com/watch?v=tRWX21lW_bU is a good video I would recommend for anyone in your position.

Helping myself physically helped me mentally. And that's good because I didn't have to think much to help myself physically, because of where I was starting, just moving at all was a good accomplishment.

I hope that helps, I know everyone says exercise but, to me, it lacks meaningfulness when it's not explained. Good luck.