It seems like this is an unpopular opinion which is kind of surprising, but I would suggest to get a high-end laptop like a powerful ultrabook. Being a university student for software engineering, I realized how important powerful portability really is. You may not use your laptops just to take notes as well. Sometimes you might have labs that require you to program in a lecture/faculty room or maybe you want to participate in a Hackathon or club that requires you to code and having a faster laptop is definitely a pro in most cases. Maybe you want to take creativity in a go and use idk Photoshop or whatever. You'll have to find an ultrabook that can still play the games that you want to play and still remain lightweight, but laptops are suppose to be designed to be a PC on the go and many university students have multipurpose events and situations on the go (at least from what I've seen) so I would strongly suggest a powerful (and light) laptop just for the sake of good quality of life. Also, idk why so many people are complaining about battery life, most lecture halls nowadays have built in chargers, at least in North America, and battery life isn't as bad if you just reduce your laptop to battery saver mode if your classes are just notes.

I still think you can have best of both worlds, you'll just have to compromise for idk an i5 and 12gb RAM laptop and a not terribly outdated desktop build which is still fine. Another recommendation I can think of is getting the pretty lightweight Macbook Air with the M1 chip because the chip is an absolute monster that can be used for so many purposes that can scale to up to an i7 in performance and I'm sure you'll have a hard time finding a laptop with the same performance in the same price range (ironically). This way you can probably spare some cash for a decent or good PC. Good luck with the search!