This is an actual first-world problem, and dealing with it is going to be one of the most important and interesting challenges of the next 50 - 100 years. I see technology continuing to improve productivity, drive down demand for labor, and exacerbate current inequality issues.
Our economic system isn't really setup to work well in a situation where supply of labor drastically exceeds the demand for it.
Specialisation is a form of skill and so the issue is really what happens to unskilled labour. Everyone "knows" that education is a fix, but current education systems are extremely broken and closely modelled on the dawn of the industrial age https://www.youtube.com/watch?v=zDZFcDGpL4U
It will be interesting to see if the cost of living goes down since that will also greatly alleviate things. Increased automation should result in that.
Unless you start out with piles of capital, you have to get paid for doing something in order to pay for things like food. If your labor is worth almost nothing, you will be doing a lot of it in order to cover basic needs. That is only prosperity for people who have the capital to take advantage of low labor costs, for others it is hand to mouth.
There isn't any reason to suppose that demand for engineers and managers will ever come anywhere close to 100% of the working population.
Meanwhile, the advantage of theft, violent crime and the black market improves dramatically as wages decline to nothing.
You are assuming capitalism for everyone which is not a given. Heck it isn't even how things are at the moment. It is increasingly possible to shift the proportion of people paid for labour/capitalism to being supported by the state. If the costs of living go down (a likely consequence of increased automation) then the financial burden would decrease too.
This is a frequent but incorrect and dangerous claim because it assumes that a capitalistic economic system is necessary and immutable when in fact that is not the case.
Incorrect because if productivity were increased to the extent where labor costs were no longer a part of the equation, then humanity would not cease to exist as this claim implies (i.e. no jobs begets no money begets no food begets mass starvation begets extinction).
Dangerous because this line of thinking drives protectionism (i.e. unions, trade barriers and tariffs, subsidies) which increases the cost of goods which provably does lead to homelessness and starvation. This is not to say that tariffs and such are intrinsically bad because there are other factors involved (e.g. national security), or that increases are not eventually offset by corresponding decreases as competitors enter the (free? maybe...) market. Nonetheless, people suffer until the eventually happens.