No, it won't look exactly like moving from human computers to machine computers. It won't look exactly like moving from manual farming to tractors and combines. It's hard to imagine what it will look like, but it seems overly pessimistic to just assume that this time automation is going to turn out terribly.
The issue isn't how to keep people busy. That's not a very worthy goal. In the '50s we dreamed of a society where robots took the yoke from our shoulders and let us live better lives. Now that it's happening, all we can talk about is how to get people back to work!
How many times do the same predictions have to be proven false before we don't take them seriously anymore?
People won't do that though. We will continue to hear the same predictions for another hundred years, and every time the people making will say "but this time it's different!"
Everyone always says that these people are just suffering from a skills shortage and need to retrain into a different career and move to where the jobs are. But which careers should they choose to retrain into? Retraining represents several years of time investment and at least tens of thousands of dollars in money investment, money which they don't even have in the bank, so choosing wrong will often be the last nail in the coffin. When I was entering school I was told that going into CS was too risky because everyone was offshoring these days. Instead the most recommended "safe" jobs were: lawyer, pharmacist, welder. Of those three choices, only one was still in demand by the time the entering cohort had graduated. The other two had such a glut of entering workers that many new grads were being advised to retrain again. When industry demand is changing faster than people can reasonably retrain and pay off their student loans, "skills shortage" is just another way to say "let them eat cake", and the pace of automation is absolutely contributing to this issue.
Saying that it happened before is not really convincing either, unless we understand the underlying mechanism and can predict that it will continue to operate the same - and I haven't even seen any convincing theories yet. Relying on past observations alone without understanding what's behind them is not always such a good idea; you might be crossing the river by walking on ice because it never cracked before - and then one day it does, because it's springtime. If the risks are high, I'd rather be more sure than "it never happened before". And we're talking about a potential economic disruption so massive that it'd likely erupt into violence, so the risks are high.
The burden of proof is on you, if you want to argue that the limits of growth are right around the corner.
I have been hearing people yell the the same arguement that you are making about infinite growth for years. And yet every year they get proven wrong. So talk to me in a thousand years, when we actually start to hit those limits.
Same "fears" different century.
EDIT: more thoughts
I just finished reading an Asimov novel written in 1955. There were computers in this book. They were people. Computer was a job title. Now we have machines that do that job, and we have an entire new industry employing lots and lots of people that didn't exist before that one job, Computer, was automated.