How much of a refund did they ask for, and how much did they get?
Before that stay (I'm the OP's roommate), we stayed at another apartment that had 0.5Mbps Internet instead of the claimed 10Mbps, no hot water, no computer desks when there were desks in the photos, no trash cans - for the first 3 to 5 days until all these issues got fixed through us bugging the building's management. All Airbnb was willing to refund was 10% of the nightly cost, times some number of nights, which amounted to USD 57. That was for a $2100/mo apartment.
Because there was no "laptop-friendly workspace" in the bedrooms. The host claimed that in the listing, and the only thing that remotely qualified was the dining table in the kitchen.
Not having the ability to specify 'Partial A/C' is exactly my suggestion to Airbnb.
The "reasonable solution" didn't work - we waited longer than what the host claimed it would take to make the place "cool as a fridge".
Why would we not be supposed to work in the apartment?
Right, it wasn't anyone's hard fault, so if I were the host, I'd charge 3 nights' worth and leave the situation with a clean conscience and quite a bit of cash for spending 30 minutes.