State provided education is ancient in Germany, though, but implementation was spotty. Luther (yes that one) called for universal education in 1524, calling for six hours a day school for boys and one for girls, all learning to read and write and the boys maths and physics and stuff (the girls would be taught home economics at home). Pfalz-Zweibrücken were the first to introduce universal and mandatory public education for both girls and boys in 1592, not just in Germany but the world. There had been separate curricula for boys and girls until 1970, alas they largely threw out much very useful stuff in the unification process. Like home economics. But I digress.
As said though implementation was spotty (and way worse in Catholic areas than Lutheran ones), there initially also was resistance from the population, but it took up speed after enlightenment. In 1816 Prussian statistics said 60% of kids attended school, raising to 82% in 1846. This is approximately the context that SDAP demand is to be understood in: They wanted proper universal education, seeing the difference it made. It doesn’t really matter where you learn to read and write, it’s still learning where to read and write. Universal secondary and higher education were still way off by then.
All in all this is rather rich coming from Marx, himself very much part of the educated elite: He studied law at university, whereas a significant portion of workers didn’t even visit primary. Engels, you know, the bourgeois fat cat, actually had a way better grasp on the Lumpen than Marx: His family was pietist and as such he spent his childhood years visiting a public (not private) school and playing with worker kids, despite his elevated socio-economic status.
Which actually brings me to another particularity of the German system: Visiting a school is mandatory. There’s been cases of US-influenced fundamental Christians wanting to homeschool because “public schools teach witchcraft” (you know the type), every court they appealed to didn’t give a rat’s arse about the parents opinion but ruled that the kid has a right to attend school and be exposed to the majority population, even if that’s to learn to valiantly stand firm in the subculture their parents want them to be part of. They ultimately seeked asylum in the US, where they’re a playball of the culture war there – they could’ve just moved to, say, Austria, and wouldn’t now face deportation.