For whatever reason, this company is paying for your time, not your work. In my industry, we call this, "Paid to wait". I don't agree with the inefficiency of it, but some companies want a person available, even if they don't have full-time work to offer. That's okay; jobs owe you money, not fulfillment.
I once took a job, and on my first day, the boss said, "The hardest part for you is going to be learning to back off." You've got to adapt to your workplace culture; you've got to back off. It's okay if this company can't use you, because, with a slight adjustment to your thinking, you can use them.
You don't have to "waste away the day". You say, instead of sitting at work with nothing to do, you'd rather use that time to start your own consulting business, and look for another job. Can't you do these things AT WORK? A lot of certifications can be done online, too. Wanna learn a foreign language? Duolingo! According to you, they're not monitoring you very closely. You could be getting paid to do what you want!!!
If they decide this is a problem, and fire you, why would you care? You want to quit anyway.
This is a golden opportunity. Don't squander it.