> is there like a list of things that government is responsible for

Why yes, there is. Here's an example of that list for the federal government [1]. States and cities also have similar lists though they may not be as accessible to the general public (a problem to be sure).

> or is it just vibes? if not, how is that not rife for abuse?

Not really vibes, it's spelt out in statute. In some cases that responsibility can be pretty wide and in all cases the president can chose heads of office that don't care to or ignore the duties of those statutes. The remedy if you feel like that's happening too much is voting.

> how is that not rife for abuse?

Abuse can certainly happen. However, the US does have some inordinate amounts of oversight over federally ran programs precisely because a lot of people worry about abuses. Where the abuse tends to happen is when the US is funding private institutions rather than running the programs themselves.

I have family that currently works for the US gov writing software. As they tell it, it takes 3 weeks to bring in a new version of a library due to the mandatory review process in the statutes. Meanwhile, they can hire a contractor who can use any library they like (but also who can bill whatever they like and are often friends with senators).

> it was already the case, even with tons of funding. (in case you don't know, i have a phd in chemical biology)

It used to be much more open ended. It has, however gotten worse and it's about to get much worse. Exactly because of concerns for abuse and waste. The system from clinton to trump wasn't great but it was somewhat functional. We are about to enter a new era, however, where funding for grants can be axed while the research is in flight if the administration decides that they don't like what's being researched. That's the abuse and waste I'm actually worried about.

[1] https://www.law.cornell.edu/uscode/text