One way to handle the problems with building a city deep underground would be to build a city on and above the surface with a really deep city wide basement.
If the air in the vast basement region is always at the same temperature, it can be sucked up and circulated near the ceilings in the summer to cool rooms down, and sucked up and circulted near the floors in the winter to warm rooms up.
Additional heating and cooling of the air from underground would be necessary at times, and would be most efficient if done by neighborhood or city scale heating and cooling units.
Presumably the vast city basement would also contain vast pools or tanks of waters, since water retrains heat, and it would further moderate the air temperatures in the basement.
New air would need to be sucked into the vast underground basement and should be sucked through filters to filter out dust, pollen, spores, and various undesirable gases.
And the streets of the city could be underground, connecting the basements of the various buildings in the top levelof the city wide basement, and there could be storm shelters in the top levels, while most of the basement levels would be vast air spaces.
And such cities might be the first steps to building totally underground cities.