The answer is we just keep redefining (legally, socially and morally) who the labor force is to hide that fewer and fewer people are employed. Compared to previous eras when 100% of humanity worked from the moment they could walk until they died, we have only about 50% employment (US population 325 million, labor force 157 million).
Yes, because they are either retired/too sick (no longer able to work and in some cases forcefully stopped working so younger people can take their place to work) or students that are preparing to enter the labor market as skilled workers as opposed to unskilled workers.
Those that can work and don't live on a social security may or may not be slashed in the next election cycle to garner the votes of those that do work and in order to balance the budget. Even in Europe, social security for the unemployed is considered a temporary thing until you get a job. And many European countries are struggling to upkeep just that, with constant grumbling about the topic (look at the UK, there isn't a day where there isn't criticism or propaganda about the system).
In my country, they thrown it out and told that unemployed should work for the government as "common-workers", barely-paid people who work in
terrible conditionsthat is remiscient of Soviet times.
What's worse is that those that get into the system have are inhibited from finding proper jobs.
Art and science.
Both are technically skilled workers. They need to be taught to be able to do either and you need above-average talent/ability/investment to make it work. And no, being self-taught still requires investment to do because they take tiem.
Look at webcomics, where you would think there would be a low barrier in entry: the people that manage to make a living out of it are usually well-educated comic-book artists.
Probably a whole ton of odd jobs and the like
Which is actually an unreliable, unstable existence even in the first world.
think what self-employed folks do in the developing world cities. Some of them would be slightly better and run their own side or main businesses, and so forth.
Again, self-employed doing what? In your example 99% of all jobs is automated and the remaining 1% requires extraordinary skills and abilities. What do the people that don't have that do, what can they do that cheaper robots can't?
Art and science. Sex-work and psychiatry. I don't know, what do people in post-scarcity sci-fi stories do?
Whatever the writer imagines them doing and how idealistic does the writer imagine things. In more idealistic settings people live in communism. In slightly less idealistic settings they turn to violence and self-destructive excess out of sheer boredom. In not very idealistic settings they became punks, beggars, criminals and people that live in constant poverty while the select of the population lives in luxury.
So, not very encouraging comparison.
This is a weird comparison, but an example of the whole "everyone is self-employed because robots" thing might exist in Star Wars. Have you noticed how basically anyone in the Star Wars movies who isn't a government employee/politician, slave, or rebel is self-employed?
That's because of story-writing reasons: it's easier to garner sympathy about self-employed or family-business working characters than it is people that work for the many faceless corporations that exist in Star Wars. Not to mention the abundance of people that work the galaxy-spanning government whether it's the Empire or Republic.