I had 3 large dogs in a flat for a while, there was a garden but like PP it wasn't as easily accessible as opening door so quicker to just take them up the street for toilet trips and it quickly get used to it.
It's more a problem for the owner than the dog tbh as you have to quickly take them out first thing and maybe wandering street in PJ's at 3 am with multiple dire rear trips ahead. If your ill (virus may both be sick) that will be time you wish you had a garden. The dogs enjoyed all the fresh sniffs and sights, plus were always more likely to toilet quicker when out for walk than in the garden as they'd find some scent to over mark. It helped as they aged too as lots of short walks out is better for mobility with arthritis than usual 1 or 2 longer walks a day.
It's a shame your DH doesn't like greyhounds as sighthounds are more cat like in nature so they'd probably gel and tend to be lazy inside. Lurchers are sighthound mix so come in different sizes /looks/ stamina/ brains based on their make up genes which often not straight x but mix. Traditionally for hunting it was typically terrier or collie added in. Anything crossed with a sighthound will have similar lean bodyshape though so do see shepherds, mastiff, labs, spaniel, poodle x lurchers.
I think you can have a dog but may need to compromise on breed type, I would look for more low-medium energy breeds that you can keep fit and entertained more easily than those with higher energy/stimulation needs that will struggle if you aren't able to meet them. As a first time owner its very easy to over estimate what you think can provide and manage and in reality that bright interactive, high energy dog may not be what you'd enjoy living with daily.
Maybe use this time to try and meet more owners of breeds that think maybe suitable in person. The breed rescues often give the more negative aspects as want people to go into adoption with realistic expectations.
The good thing about going with an adult rescue dog is that you've a better idea of what to expect and some may not fit typical traits or energy of their breeds. Breed specific or smaller rescues are more likely to consider unusual adopter situations than larger names. If you can make the small outside area more secure from escape that will help.
Lots of dog friendly holiday accomodation and pubs etc for weekends/holidays away. Stayed in few chain hotels with dogs when visiting family in the city outskirts too.