I have a family member in Healthcare (nurse practitioner) who in all likelihood just has a sinus infection, but regardless had to take a covid test to prove otherwise. Their employer is using a 7 day covid result test and until the results are in from the lab they are being forced to take personal vacation days while being told to stay home. This is happening in Ohio if it matters at all.

As an outsider looking in that doesn't seem ethical in the slightest. Using a testing method that takes an extremely long time to process when there are quicker tests available then making your employees burn through all their personal vacation days? Is that legal?

Yes.  It's also a good way to guarantee that once the job market improves your employees will flee for greener pastures.

Are the quicker turnaround tests significantly less accurate?

According to a friend that works for a medical supply company, they are all just as accurate. Also as a aside fun fact, from my family member that is the practitioner in question, they sent in 2 unused covid tests for testing and the results came back positive for covid... so ya they are some really accurate tests to begin with.

I think it's quite a stretch to claim that the employer chose the longer test just so they could fuck the employees out of their vacation time.

I think you'll have a hard time finding a lawyer to chase that one, although if you look hard enough in the right level of the profession, you may find one.