the relevant field would be microbiology. while someone who got all the way past about the first semester of organic chemistry lab is perfectly capable of making some rudimentary chemical weapons, they won't necessarily be able to make it safely, reliably, cheaply, consistently, and without killing themselves, and universities most of the time put enough sense in everyone's head to not do that. this strictly requires that you know anything about chemistry, too. for bioweapons every single problem pointed to above is orders of magnitudes worse, and you probably need masters degree to do anything seriously nefarious. then you get into the problem of using that stuff, and you need explosives for that anyway. the reason for that

(Also I think there is a good reason we don’t really see terrorists use biological weapons, nor chemical weapons (with a few notable, but not that effective exceptions), big bada boom is king)

is that barrier to booms is even lower, especially if your country is strewn with UXO. there's also an entirely different reason why professional militaries don't use chemical/biological weapons https://acoup.blog/2020/03/20/collections-why-dont-we-use-chemical-weapons-anymore/