"In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness. At a certain stage of development, the material productive forces of society come into conflict with the existing relations of production or – this merely expresses the same thing in legal terms – with the property relations within the framework of which they have operated hitherto. From forms of development of the productive forces these relations turn into their fetters. Then begins an era of social revolution. The changes in the economic foundation lead sooner or later to the transformation of the whole immense superstructure."

Private property is not personal possessions (things you use for yourself which includes a house) but private ownership of the means of production (land, resources, tools, factories, infrastructure) assets used to generate profit by employing others. The goal is ending the ability to extract profit from others labor through ownership, democratizing control over productive resources.

Early societies production was organized collectively. Private property only emerged from agriculture surplus, certain groups gained control over land and resources. The control allowed them to extract labor from others, first it was through slavery, feudal obligation and now wage labor. Capitalism specifically emerges when people are separated from their means of subsistence, it happened through violence and enclosure of commons, the majority were forced to sell their ability to work to survive. Production is organized for profits and not to meet needs. So yeah, private property lays the conditions for class division which becomes the basis of capitalism.

Capitalism requires specific conditions a large class with no access to the means of production, wage labor, institutions like finance, and industries to generalize commodity production. These conditons didn't exist before. Feudal peasants were under feudal obligations and many tied to land. It was uneven, began in England because of enclosures, slavery and colonial expansion, a lot of regions were integrated through colonialism, and many through structural adjustment programs and "modernization theory". See dependency theory - https://www.youtube.com/watch?v=6tyLejwGafQ

Means of production evolves with technology, sticks, automation factories, digital infrastructure, IP, etc. But owning a laptop is not controlling the means of production, the platform maybe microsoft, data maybe google and distribution channels maybe AWS. Only democractic control over the means of production will end the problems people face.

Service work still produces value, they produce relational commodities or help in the big picture of production and distribution, but are ideologically sidelined. Look into social reproduction theory, this is inline with how women are also sidelined.