The Roman empire, which existed from 27 BC to AD 395, had Rome as its capital, and while numbers are subject to discussion given the age, the floor for the density of the city of Rome back then, which had a large number of insulae, or apartment buildings, is 30,000 people/sq km. A more recent estimate put it at 72,150 people per square kilometer *. For reference, Manhattans' population density as of the 2020 census is 72,918 people per square kilometer.
This was 1,600 years ago! That is to say, there is precedent for humans living in the kinds of densities we have today, without anywhere near the kinds of technology we have. There was no electricity, no cars, no Internet back in '400. They most modern revolutionary thing was running water, and even then they used lead pipes for it and had no electrical pumps to pump it up to the 9th floor. One thing that will be familiar to modern readers is that the government came in and imposed regulations, making some buildings illegal due to height restrictions.
* https://go.gale.com/ps/i.do?id=GALE%7CA20586744&sid=googleSc....
Also, the population of Rome collapsed less than a century later.