OK.

I'm not going to code up a simulation because the research hasn't been done to confirm my choice of constants, but I can sketch it. Each workday is a function of the macroeconomic climate and some set of cultural norms during which we exhibit some blend of the following personae. As we'll see, introducing UBI reduces the prevalence of the bureaucrat persona which has knock-on effects leading to surplus.

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The Missionary - has a mission and is working towards it. Cares more about the mission than prestige.

The Worker - doesn't have a plan, but likes to be a part of something meaningful. Will gamble with prestige in order to ensure that the work stays meaningful.

The Bureaucrat - willing to tolerate or create waste in favor of preserving prestige. Sometimes manages to trick a worker into believing they're a missionary.

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Obviously people are more complex than this. Also, I'll use dollars to indicate productive output even though I think that most of the time collapsing such things to a single dimension is a slippery slope to somewhere awful. All this to say: gimme a break, it's model.

Here are my totally made up constants, note that X is a parameter which will depend on UBI:

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Missionary creates 100$ of output always, plus a 1% daily chance to inspire a worker to become a missionary, a 1% chance to inspire a bureaucrat to become a worker, and a 1% chance to burn out and become a worker.

Worker creates 80$ of output if they're following a missionary and -20$ if they're following a bureaucrat because it's likely that they're causing more harm than good. They have an X% chance of burning out and becoming a bureaucrat.

A Bureaucrat creates -$20 of output, because they're definitely doing more harm than good.

Now lets say that everybody consumes $5 each day to stay alive.

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So X is our worker burn-out rate.

As with most systems of this kind, it's very sensitive to initial conditions. If you start with a high enough concentration of workers and missionaries, your bureaucrat rate will be very low and you'll have a surplus. Too many bureaucrats and most of your workers are doing more harm than good, the system is carried (if it survives at all) by the missionaries and the minority of workers following them.

Critically, X is a function of risk tolerance. The worker becomes a bureaucrat because they cannot tolerate the risk of pointing out the wastefulness of the bureaucrat above them.

Introducing UBI does two things. It makes standing up to your Bureaucrat less risky, reducing X, and it creates a fourth type, the Video Gamer, who consumes $5 to stay alive but doesn't sabotage the output of any workers like the bureaucrat does.

Some percentage of the Bureaucrats will become Video Gamers if UBI is implemented. That percent depends on the size of the surplus. If the surplus gets big enough, UBI can be so comfortable that there's no reason to be a bureaucrat, because it doesn't afford a significant quality of life increase.

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So to answer your question about the 3M and the 210M, I'd guess that today we've got 213M people living on the positive output of maybe 50M--the rest are bureaucrats or are following bureaucrats. They're busy fighting over their slice of the pie instead of baking it. Bureaucrats sort of expand to consume available resources, so as automation improves worker output, that ratio will get worse unless we find a place to put them.

We'd have to do research to come up with better constants and run that model for real to be sure, but I don't think it's unreasonable to assume that reducing both the bureaucrat concentration and the worker burnout rate by 50% would triple the system's output once you let the personae conventions find a new equilibrium. I'm not sure how much more federal employees will get paid above UBI, but I think there's room for the end result to be that future UBI is cushier than today's government work.