Overengineering a way to know if people are in my university's CS lab

Nice project but it could be illegal. Check your jurisdiction.

Source: have done similar hobby projects for fun, which turned out to be illegal.

this isn't facial recognition

???

Who's talking about that?

why would it be illegal?

Generally, you cannot just record people without their consent; but this also largely depends on the jurisdiction/situation.

Almost nowhere (or actually nowhere?) are you allowed to set up a surveillance device into a space that is not public and it is not owned by you.

Public university labs are generally public as they're state property (in this particular case, UW Madison is a public state University). Further, recording video or pictures of people in public places is broadly legal in the US. There are only "presumption of privacy" restrictions which apply to places such as bathrooms and private property that is not visible from a public location (ex. a sidewalk).

Obv. IANAL and this is not legal advice.

By this logic the dorm room bathrooms at public universities are also public and I should be able to setup cameras /s