My kid taught at a large state university and always changed the test between sections. I assumed everyone did. Some high school teachers are lazy on this, in our experience, causing rampant lunchtime cheating conversations.
I think the best programs have steps in terms of consequences. Some students need to be educated so a first step should be an education program in whatever form, about what cheating is, what plagiarism means, and what will happen if it happens again.
Then the consequences vary from F’s, suspension and dismissal. The Ivies seemed especially strict but I would think many LAC’s would be too.
I don’t know how you choose a school on this basis. Many have honor codes of one sort or the other. I think my kids just did what they did (honest I believe!) without regard to others. Education isn’t a race, or it shouldn’t be. There are so many other criteria. You said money is okay, but size, location, academic majors and curricula, and “vibe.”