You've just described the basic setting of Paranoia.
If you read that description a bit, you'll notice that the personality of your all-controlling AI is going to have a major effect on what the jobs are and what life is like. In Paranoia The Computer and its bots are capable (and sometimes do a decent job) of taking care of the basic needs of all citizens: Food, clothing, and shelter are all available more-or-less in abundance.
But The Computer is also insane! It was programmed to keep everyone safe from the commies and happy. So now happiness is mandatory! Failure to be happy at all times is treason! Traitors are executed on live television as examples to others, thereby making sure the population remains always at peak happiness. Commies are also traitors. The Computer regularly sends squads of "Troubleshooters" to infiltrate and destroy any Commie cells out there. Squads that find no such cells are obviously traitors themselves and will be executed. The Computer knows they're out there, not finding them is a sign of collaboration.
Jobs in this kind of AI-controlled dystopia consist of "Do what you're told" and "Find ways to avoid being executed for things beyond your control." The rules are arbitrary, contradictory, and subject to change retroactively without notice.
Worship of the AI by the humans is quite likely to eventually lead to this kind of world as they dump decisions on it that it was never intended to process, doesn't know what to do with, and solves via methods reminiscent of the Literal Genie from your favorite TV show. Worshiping the AI as a god is going to prevent any attempt to correct these mistakes, and the end result will be very much double plus ungood.
On the other hand, if your AI just makes sure that sufficient food, clothing, and shelter are always available for the population, and isn't vicious and arbitrary about how it achieves that goal (it has common sense and/or can be corrected easily when it misbehaves), then what you'll get is a "post scarcity" society.
What would people do? What would you do if you suddenly didn't have to worry about the basic necessities of life? Would you take up painting? Mountain climbing? Start working on interstellar spacecraft just to "see what's out there"?
If you use Tom Sawyers definitions of "work" being "what a body is obliged to do" and "play" as "what a body is not obliged to do" then there is going to be very little work that even bears thinking about in this world. Do what you love, all else is a waste of your limited lifespan.
There will still be an economy, because nothing can ever be infinite. But it will be mostly trade in things that today we would consider frivolous. Why pay someone for hand-grown produce when as much food as you want is available for free? The same reason rich people today spend thousands of dollars on badly-hemmed scraps of cloth just because it's called a scarf and has a designer label. Why do things for others at all when all your needs are met by the AI? Because humans have a drive to acquire social status and being good at doing something (even something objectively useless, look at sports players) is one way to achieve that. Sports, entertainment, art, and exploration are probably going to be the major categories of serious things that people do.
Of course, all of those categories will probably be small compared to "Lounging around and getting fat." It all depends on what's appealing to individuals.
For meditations on a post-scarcity society that are also fun to read, I recommend "Voyage from Yesteryear" by James P. Hogan.