The logistics of a super-deep city is very non-trivial.
A normal car engine uses 9m3 of CO2 per minute, or 0.15m3 per second. If you have a pipe that has a diameter of 0.55m (an area of ~1m2), the air will move at a leisurely 0.5kph. That's not to bad, right? But it's a single engine. If you have a whole city underground, you need a lot of air. 10 cars and your pipe now runs at 5kph. 1000 vehicles and your 0.5m pipe is at 50kph. In a modern city, cars are super-common (80% of adults have a car). So if you have a city of 10,000, you've got 8,000 cars, and you need 1200m3 per second. If you have a 10m wide ventilation shaft, the airflow will be about 3.8kph.
There is a mass difference between CO2 and O2, and this means that you need to pump that mass difference up your ventilation system (an extra 0.6kg per m3 of CO2), and where that mass comes from? Burning the fuel in engines introduces the carbon into the air. By the time you're 10km underground, you have a pressure of 58kPa of pressure from the mass difference. This is about the same as a soccer ball - not to much, but way more than a simple fan can produce. You actually need a pump that can provide pressure.
A long pipe has fair amount of resistance. Blowing air through a drinking straw is easy enough. Blowing air through a 50m hosepipe is another matter entirely. By the time you've got 10km of depth, you're going to need a fairly enormous amount of pressure just to drive air down there. You're going to need stages of air-pumps. But those air-pumps need engines to drive them, so you end up with a situation similar to the rocket-law. For every extra pump you install near the bottom, you need a whole bunch of pumps leading up to the surface.
You are moving literal tonnes of air under reasonably high pressures up to and down from the surface. I honestly can't imagine the scale of a system needed to drive air down to a city 10km underground. It would involve power plants, HUGE ventilation shafts, and endless arrays of turbines after turbines.
Then there's the other logistics: water, food, transport. How do you get people to the surface? Elevators are limited to about 500m by the tensile strength of the cables (a long cable will snap under it's own weight), so you'd have a chain of 20 elevators to go 10km underground. At each stop you'd have to get out, wait ages for the next one to arrive and ride it down. Seriously, just build a 100km road with a gentle gradient and set up a bus system. Great, more area that needs ventilation.
Supplying water is another interesting one. A normal human can use way over 100 liters of water per day. Assuming a society where water is precious, you can get way lower usages, but probably 30 liters per day is pushing it for a good level of hygiene. So to supply 10,000 people, you need to provide 300,000 liters of water per day. Underground streams? I consider that unlikely at 10km depth (but in all honesty I know nothing about geology). Running a pipe vertically for 10km will create a pressure of 100MPa. That sort of pressure is lower than the tensile strength of steel, but you'd probably want a bunch of stop-off dams mid-way down to avoid having ridiculous wall-thickness pipes. More amazingly massive underground infrastructure
For reference, the deepest mine us humans have built is only 4km deep. You can read about it here: https://en.wikipedia.org/wiki/TauTona_Mine but they need air-conditioning to cool the environment, and it takes an hour to get to/from the surface.
When reading on other deep mines, you find quotes like:
The mine also built the world's largest ice factory which produced up
to 8,000t of ice daily to cool wall rock temperatures (50-60 deg
8,000 tonnes of ice? Wow. It takes a serious amount of energy to do that.
So, how deep? I have no idea, but the infrastructure your dwarves would build in their pursuit of depth could easily dwarf anything we've built today (pun fully intended).