How does HN intend to control the population with small government that respects a free market and civil liberties?
A bigger safety net will get more people into college or careers so they'll be too busy to have kids for awhile, and will start a family in their 30s and then maybe only have two kids, if people are slaves to wage then they almost have to get married early to even afford a place to live and that often leads to children not long after.
A comfortable and happy society is a well balanced society and will have more natural population i.e. something close to repopulation quotient.
I don't have stats on this but maybe compare countries like the USA with Finland, and Denmark which often rank top 10 on 'happy countries' lists.
If all those things exist, then you can work on making it so there's still strong government, but the city has checks and balances that on some issues makes it more powerful to enact laws than the state, and the state, is the same to the federal.
States would be more like EU members, Fed would be like NATO and IMF - i.e. protection, foreign affairs, and military protection should be it's major concern, and policing that every state has a way to guarantee the rights previously mentioned.
For this to work, I think we also need to stop giving subsidies to corps, instead give them to work-owned co-ops and unions of co-ops that give back to customers/employees and help pay for the healthcare and housing (or UBi benefits), or we lean on the idea that land is a public resource and apply a land value tax, so mostly the rich and corporations pay for the needs of the rest of us by the value they get out of the land.
As for controlling population, I don't think we should but we should figure out a better system for managing populations, pollution, waste, and possibly settlements in space if feasible (if we can get gravity to work for bone/muscle issues). A solar punk future looks way more pleasing though than a cyberpunk one. If you can merge left-liberarianism, socialism, capitalism (via co-ops and still a free market just with more worker-ownership similar maybe to how everyone used to have pensions and stick with a company a lot longer), and georgism with universal basic income/healthcare, then we might be able to live in a better world.
Every child on earth should have equal access to education and be encouraged to go into the sciences unless they are super artistic or have other talents but we can't go wrong if we have 8 billion and 75% of the adults are scientists or engineers, or stay-at-home parents (as that's important for quality of life too), in the 50s it was normal a family could afford to keep one parent home, not anymore. GBI gives more opportunity to pursue things like doctorates, artistic endeavors, and entrepreneurial activities.