In most states, breaks are required by law. The employer has to, by law, enforce that employees take those breaks. If they fail to do so, it opens them up to very expensive lawsuits. I recall a decade or two back, The Gap has a massive settlement in the state of California over employees working through breaks.
It refers to "being at work", not "actively heads-down working on something". If you come in at 9am, do work, have lunch, make coffee, work more, suffer meetings, work, chat at the water cooler, work again, and leave at 5pm, you're working 9-5.
Federal law does not require lunch or coffee breaks.
There is no federal law or Arizona state law that says employers must provide breaks and lunches. There are mandatory break and lunch period laws in some other states, but not Arizona.
Employees must be allowed a meal period when they work more than five hours in a shift. A meal period must be at least 30 minutes long and start between the second and fifth hour of the shift.
An eight-hour workday is a standardized work schedule in which an employee works for 8 hours per day. An employee who works an eight-hour workday will often work five days a week with two days off. This is sometimes known as a full-time job or working a 9-5, which means working 8 hours a day between 9 am and 5 pm.
If HR won't help you, go to your local labor board and report them. And if you do go to your local labor board, talk to a lawyer and let them know what's going on. Also, try and take your 30-minute breaks to show that you're following the law or at least trying to. Plus, it'll give you more evidence against your boss.