I've lived in a country with socialism for my entire life, and have studied the laws in my own and other countries without socialism.
I will talk about socialism as it is in Scandinavia, more specifically Denmark. Here's a few things other than paid education and free healthcare:
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Getting paid to study: You get paid to study as soon as you turn 18. In that way you don't need a job while you studying. Basic salary when living away from parents: 1.000 USD/month.
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UBI: In Denmark we have UBI for people being poor, basically. If you don't have a job, is sick and can't work, or any other reason you might be screwed, you get paid by the government to... well yeah, exist basically. You have to meet some requirements and actively trying to get better or find a job though, which seems fair I think. If the government thinks it's not possible to get better, you can get the money permanently for the rest of your life without doing anything. (this is used for people with disabilities, both mental and physical, both born with it or obtained later in life)
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Shared heating system: This is maybe the biggest "socialism" thing I can mention. In Denmark your house or apartment can be hooked up to a country wide heating system, which means we all share the same heat. This is a way to make heat distribution centralised, which has major advantages such as; price, availability, maintenance. (Fun fact: every data center build in Denmark needs to be hooked up to this system, as they will "donate" all their excess heat from their servers to the central heating system)
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Flex jobbing: If you are no longer able to work 37 hours a week, you can be a flex worker. This basically means that you can work 15 hours a week and still get paid a full salary. The government will cover the rest of the pay and also cover some expenses for the company having the flex worker. This system is great for peoples mental health, as they still can feel a part of society even though they can't work full time. While they still can live a worthy life because their pay is fine. It's a win-win for the country, the companies and the people needing this.
I could go on, but I don't want to be that guy praising my own country all the time. We Scandinavians tend to do that.