I think to explain the concept you've got to start it little broader. Like if you were to supply for yourself it's all simple, you produce, what you consume and your production is done, planned and performed by you and necessitated by your needs and desires.
The problem is that it is terribly inefficient. If you would ACTUALLY do everything all by yourself and not just pretend that and use other people implicitly, by idk having an income and buying stuff, but really actually do everything yourself. Then you'd probably not get beyond a very primitive life that is mostly concerned with immediate survival.
And that's already ignoring that you have to start from somewhere and that if you were just dropped into this world with no parents and support you would probably just have died before you could have had the first thought that you remember. Like even the development of the most primitive tools might have been the result of longer research by trial and error.
So instead of doing it all by yourself, you form social groups. And here thing gets more complicated, because while you can increase the production manifold and develop capabilities that the individual would not be capable off on their own, you now have to negotiate these questions from before. Because they are no longer self-evident. Like what do we want to produce, why do we want to produce it, how do we want to produce it, who plans and who enacts the plan, how is the product distributed within society and who decides all that and how do we do that.
Now as far as I know Marx argued that the distribution of the power to decide that is largely based on the material conditions and production processes. Which is not a given, the social factors and dynamics in society may also play a huge rule but they weren't the key focus of Marx.
Now for a simple hunter gatherer society things are still relatively simple. It's still possible to formulate a collective goal (gather food) and it's still easy to distribute work and loot (if all do roughly the same thing and have roughly the same needs).
Enter specialization and support roles and things get more complicated as you've now a variety of unique roles, situations and desires. So the direction in which the collective is heading is no longer the same in which the individual would want it to head based on their own personal situation. It's rather a compromise between individuals. Also some roles might take priority over others. Like idk the smith is important but if there are no farmers, hunters whatsoever the smith is without food, without strength and ultimately without any use.
So as all need the food, all contribute to the production of the food, but some directly and some indirectly, so you can end up with a situation where those with direct access to scarce and necessary goods may lay claim to them and use the power of deprivation to coerce the rest of society to their will. Like idk offer to give part of the stuff that you claimed to a handful of goons if they accept your property and coerce the rest to do the same.
The other problem is, that while the collective workload is "non-transportable" and difficult to manage as an individual, once it's condensed into a product, you can take that and run. Like it takes an impossibly large amount of labor for an individual to build a car, but it takes close to no effort to steal one.
Which becomes relevant when you move from hunter/gatherer to agriculture as it takes a large amount of labor and time to cultivate the fields and it takes much less time and labor to harvest it. So it almost naturally follows to invent something like "property", either in the abstract or in the practical sense of staying at a place and guarding it against intruders.
Meaning from the mode of production, investing time to grow and then harvest, having a period of toil and scarcity and then a period of wealth where you need to keep it together to sustain the period of scarcity. A lot of social consequences follow. As said, suddenly concepts like property make sense, which would have been pointless if you're wandering. Same for the idea of military strength and human adversaries. Like previously you could simply evade conflict and move elsewhere or do a hit and run, now you're bound to a place and have to work with that. So extortion rackets could emerge as the farmers might not have the time and power to guard their property. Giving rise to modern proto-states and monopolies of violence or the fight to establish them.
And once those grow the mobsters find themselves in a position where taking stuff isn't as straight forwards as the more they take now the less they can take later and the more resistance they face and the less alternative they have. So they have to develop new means to more effectively exploit their subjects. Like actually providing services to ease acceptance or improve production and letting farmers keep stuff if possible to make them invest and grow.
So you have a large collective of people that produces, distributes and consumes products, but it's divided into those that produce and those that extort and distribute.
And from other such data points Marx conjectured that history could be sketched as a series of class struggles and that societal processes can be conjectured from the material conditions under which they produce stuff.
So idk the feudal empires were often capped in size by the sheer limit of technology, like if it takes weeks to move an army or days to send a carrier pigeon to notify someone to send an army, then the scope in which you can operate is naturally limited. So people had to share power and agency. While claiming to be king of the realm, in reality they split the realm and gave vassals a share in return for loyalty and fees and either tried to keep those in-check by pitting them against each other or the other way around the vassals themselves put up a king to serve as a puppet and front for their goals.
So as colonialism and the industrialization yet again changed the economic condition so did the social conditions, where the middle class of merchants, craftsmen and other capitalists dethrowned the agricultural aristocracy, demystified their lore and took their place. Though as they also increased the ruling class in size and broadened participation, sporting ideas of freedom and equality. Marx apparently made out a trend that the social progress goes from authoritarian to libertarian and from the rule of the few to the rule of the many.
Now with the advent of mass production and industrialization, arts, crafts and specialization where becoming obsolete and production was made more easy, yet more effective. So while previously politics (deciding the direction of society), education, research and cultural participation was largely restricted to the upper class who had the time for that now it was possible broaden the to include even more people.
Though while it could mean a decreased workload and a more equal participation, it could also mean more profit for those with the ownership of the means of production and a different form of servitude for the rest. So the simple demand is for the workers to take ownership of the means of production and thus have that agency over their production and distribution of what they produce and where not already happening by capitalists the destruction of the feudal oppression.
So as a result society would again collectively fulfill it's collective goals, but this time they'd have excess stuff so they would be free to actually have agency and due to equal ownership and democracy they would be able to decide that directly among themselves. Without a materialist necessity from a group to take priority. So without classes. At least in theory.
So to think of that in terms of "wages" is already wrong. Because wages are a facet of the capitalist system where the owner tries to prevent co-workers from being co-owners by giving them a share of the loot rather than sharing the source of the loot. In the end you'd probably still would have to distribute the stuff that is produced so you'd also get some sort of "wage" but if you are owner it would depend on the actual output and you'd be part of those negotiations.
Also whether managers perform an important job is kind of a matter of perspective. Like what these hierarchies of managers do moderately well is to provide 1 "head of state/government" with some level of control over a vast empire. Like they are kind of what the feudal society used to be. A king can't rule the realm, but he can keep a bunch of vassals in check and they a bunch of lower vassals and so on till the individual farmer or lower level of vassal looks up and sees a vast empire despite it being more or less fractured. That's how this 80/20 society works where a minority rules a majority. And the higher up the more powerful the person as they command lots of people, by proxy. Though the question is rather, "is that a good system to begin with". Do we want one or a few leaders to have that level of control, isn't that actually far too complicated for so few people to decide in the first place. Like their job is hard, but is it necessary? Do we want someone working constantly and being super rich and powerful or do we want to spread that agency over more, up to all people instead.
So do we even want to have jobs that include fucking over the supply chain and to squeeze ever more work out of employees to make profit. Like if your own profit involves your own exploitation then you might self-regulate that less profit for less exploitation is a better trade-off. While if exploitation and profit involve two different classes of people,... yeah ... you kinda have good faith in them not being assholes.
Same for armies. Do we want them in the first place? Like they don't produce nice things and they taint the nice things that we have. But even if we do decide to have them, this hierarchical structure largely served to give a king control over the entire country. So is that intended? And even if you decide that fast decision making and streamlined processes are required more than individual agency and freedom... again why is the military a good idea in the first place if you don't absolutely need it? Even then why should a general earn more? Like with regards to the importance it's a job like any other, in fact they usually have a safer position then anybody else and have agency unlike most, so in fact they should probably earn LESS than the rest. Like their "profession" is LITERALLY todays childsplay. Like modern real time strategy games are probably more complex than generals work generations prior.
So that's just a rough overview, also Marx was most likely way to optimistic in his historical materialism, there's plenty of opportunity to bomb oneself or others back to the stone age and in terms of fascism, not even due to material necessity, but just out of spite and fanaticism. And while not necessarily endorsed by Marx "just take over and do it yourself" usually let to the expected result of having to cope with the same problems as the predecessors and having it worse because of a lack of experience, legitimation and support and violence is not a good workaround.
Not to mention that humans have kinda put a question mark behind the question as to whether fulfillment of ones desires is even an attainable goal to begin with or if fulfillment of goals creates more goals. But at least to give some credit to Marx here, he didn't argue it's the utopian end, but just the next step and the description of the problems and chances of that would be the job of people living in that novel conditions.