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First of all, there is no state in a socialist utopia. Unless you mean socialist in the sense of having a dictatorship of the proletariat, but would not call that a utopia.

Usually Marxists find speculating about the specifics of the far future communist society pretty pointless. No one can really know how it will look. I would assume there would be some system to measure the society's needs and arrange what work is necessary to fulfill them to be done.

"In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor, and therewith also the antithesis between mental and physical labor, has vanished; after labor has become not only a means of life but life's prime want; after the productive forces have also increased with the all-around development of the individual, and all the springs of co-operative wealth flow more abundantly – only then can the narrow horizon of bourgeois right be crossed in its entirety and society inscribe on its banners: From each according to his ability, to each according to his needs!" -Marx, Critique of the Gotha Programme

In a socialist state people decide what they want to do collectively. So most of the time you choose what job you want to do. While the USSR did have conscription for the military besides that people were free to choose any job they had the qualifications for and university and training were free for everyone so that those qualifications did not create unjust inequity. Through consultation with workers across the Union and by having Marxist economists and mathematicians use the best formulas (that often were much more advanced then those developed by Western economists) the Gosplan would create five year plans to set targets on how much of this product or that product each region should make. Then at each individual workplace the workers in their unions would discuss how best to implement the plan given their local material conditions

unbiased AI goies brrr :party-parrot-science:

I recently read an article on Socialism with Chinese Characteristics which included this neat line

Western liberals think in terms of quarterly reports and election cycles. Eastern communists think in terms of centuries, if not millennia.

While I think the East/West division is unnecessary for my point, I feel the liberal/communist distinction highlights an interesting divide. Marxism, and by extension Marxism-Leninism, is a study of historical periods. The long trends of history which may take place over centuries. It is also firmly rooted in materialism, which means we can only predict what is next from the current conditions and past trends. We can predict that the dictatorship of the proletariat will replace the dictatorship of the bourgeoisie because we see the relationship between these two classes as well as the proletarianization of all other classes and how the bourgeoisie overcame their feudal predecessors as the leading class over the last five hundred years or so. We cannot however, predict the exact administrative functions of higher stage communism. We do not know what lower stage communism looks like and we do not know what the conditions will exist at the end of that period or even our current one. Capital could reign another five hundred years or it could collapse tomorrow. The transitional stage could take centuries, or freed from the burden of imperialism, mere decades. By the time we reach higher stage communism the Seychelles will very likely be landless and Siberia could be quite pleasant. We might be freed from the burden of landed agriculture among other forms of grueling labor through technological developments. Things could and likely will be so different that we would struggle to recognize them, just as Marx would likely struggle to understand the internet if he arose from the dead today.

If we are to take a stab at your question however, we can use the definitions Marx lays out about labor being life's prime want and Lenin's dissolution of the political nature of the state to ascertain that there will likely be someone who is happy to live in Siberia and dedicate a few hours labor a week to agriculture or perhaps the burden can be collectively shouldered somehow. Perhaps the people of Siberia would be happy to stay there and farm undisturbed by the outside world or aided by its amenities. These are questions we cannot give direct answers to, but we can predict in broad strokes.

Edit: I would like to add as well that there is always the possibility that the "higher stage of communism" is something that we may never actually be able to reach, but should nonetheless struggle towards.

The workers would decide in a utopia. Easy. Next.

Attractive people have to go to Siberia. That makes it seem more appealing and softens the blow for everyone up there. But the uglier you are, the more likely it is you get to go work in Guam or something.

No I don't read theory why do you ask

maybe by the time we have a global socialist utopia we'll have figured out how to make an AI that isn't racist

One possibility: climate scientists check how many people can be vacationing in the Seychelles at one time without absolutely destroying the ecosystem. The right amount of tickets are randomly distributed to people/families/friend groups that apply. Or first come first serve, or there's just a waiting list.

Cybernetic Workers' councils Mr. BigBoopPaul, every council gets a shiny chrome-colored supercomputer, decentralized centralization, the soviet councils will be reborn

The best answers for this probably won't be from Marx or Lenin themselves but later writers in the tradition.

I do not know who or what those answers are though.

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I'd imagine people will do what they want to do, and technology will do the jobs no one wants to do. In cases where the work can't be done by a robot, it would probably be a shared responsibility that cycles through a group of people able to do it.