Also, there's just no reason to put people on the moon, why would somebody spend the money to do that?
In an environment that large, they would probably not use CO2 scrubbers except in emergencies. They could either isolate CO2 using cryogenics and dump it overboard or convert it into methane using the Sabatier process for use in Starship. Access to cryogenic temperatures would be available during the lunar night. Otherwise they would need a heat pump to dump enough heat into the ground. Alternatively there are experiments using an algae farm, however that would probably be a much later development.
Oxygen production is remarkably easy. With water, hydrolysis is perfectly acceptable even if it's terribly inefficient. You could even feed in water left over from the Sabatier process. For emergencies, there are chemical oxygen candles and liquid O2 storage.
As for why we would put people on the moon there are several reasons. Initially tourism would be the main driver. How much would you pay to go and spend a week on the moon? There are 56.1 million people who have more than a million dollars to their name. There are 2755 billionaires with friends and family who may want to put their footprints in regolith.
More practically, there are distinct industrial advantages to a 1/10 gravity pure vacuum environment. Experiments at the ISS have illuminated a few of these things like fiber optics, chemistry, and metallurgy. Lunar vacuum is better than most laboratory vacuum chambers. In addition there are tons of scientific reasons to go to the moon. Physics, astronomy, chemistry, biology, botany, etc...
Finally, there is the Mars angle. While re-fueling in orbit using Starship is pretty awesome, being able to stage on the Moon would provide infrastructure for launches to interplanetary space. Using the Earth as a gravity assist we can launch from the Moon to anywhere in the solar system using bare fractions of the Delta-V used by Earth rockets. A self sustaining colony on the Moon would also be a great way to help man take the first steps to becoming an interplanetary species in a relatively reachable location.
