None of these Arks are going to support billions.
Anywhere intended for long-term habitation needs to be surrounded by 5m of metal or 10m of dirt (or a proper magnetosphere), and even a small amount of gravity can make life a lot more convenient in terms of having an up and down direction, not having to sleep next to a fan etc.
To my mind somewhere like Phobos makes the most sense for the first space colonies - enough dirt available to build things, not enough delta-v cost to matter.
IMHO though we live in a "post scifi" age now (2019!) and should rather discard most of the mainstream utopian/dystopian fantasies already. At least until we manage to envision some pragmatic solutions to the very real and pressing problems we have on this planet right now.
We need to work together if we want to even have a slight chance to survive the next couple of decades collectively. We need some genuinely new utopian thinking if we want us all to survive.
Most of these billionaire "backup" plans as well as middle class "prepper" movements are dangerous distractions (and unlikely to "work out" for the cohorts pushing for them anyways).
If we like it or not we are in this together.
Insects may disappear by 2100: https://www.theguardian.com/environment/2019/feb/10/why-are-...
Phytoplankton has nearly halved in the oceans since 1950: https://www.scientificamerican.com/article/phytoplankton-pop...
Wildlife is becoming paralyzed and diving because of vitamin deficiencies: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6196476/
We have already knocked out the base of the food chains we depend on- we cannot consume our way out of this hole. The future of this species is already in question, we can't afford these fantasies.