Any CPU can do that. Honestly, I'd probably recommend using Ryzen. It's going to be cheaper, and being a student you can probably use every extra penny you can save, unless you're lucky enough to have family with or your own deep pockets. Most don't.
Plus, it's not just the CPUs that are less expensive, but the boards are generally a bit cheaper as well unless you plan to overclock and go with a higher end board and cooling solution. If that's the plan, then you might as well go Intel as you'll have a lot more headroom for overclocking, which brings enough performance to put it out of the reach of Ryzen in most cases. Memory compatibility is another area where Intel is a lot more promising. Practically any memory will work on most Intel configurations. Ryzen has some compatibility issues, especially on lower end boards, and despite a series of BIOS updates since the launch of Ryzen that have improved memory compatibility. It still persists, although not to the level that it was at early on.
Gaming and multitasking are absolutely not two different things. These days, aside from productivity usage, multitasking usually means gaming while also running streams, or recording, or encoding, or browsing (Often with many tabs open), or using resource intensive overlays or a variety of other gaming centric processes, all while gaming. In some cases, doing many of these things simultaneously. In this type of scenario Ryzen is easily the better choice, for the time being. It remains to be seen if the 9th gen Intel CPUs are going to change that or not.
And just because somebody is headed to school to be a software engineer, doesn't mean that they are currently any better off than anybody else. Especially when you factor in the probability of student loans, living expenses and housing. Being a student ain't cheap. Many a student has survived on boxes of Top Ramen while waiting for the day when they can put their schooling to earning some bank.
Do you have a built already, at least somewhat semi-outlined, or is this really in the early stages of planning? Do you have a firm budget to work with or is it rather flexible? Any other considerations aside from performance and quality, or are aesthetics a concern for you as well?