I don't think it's entirely an either/or; I think you can produce while you're building soil (and also then whatever you produce will have some non-edible biomass to go back into your
compost piles!).
The soil-building you're doing sounds great. When I moved into my current place, the garden was entirely under paving slabs, and when I yanked those up, underneath was good solid compacted London clay

I went for raised beds and just dumped lots of stuff on top without bothering to open the clay up at all. 3 years in, you can get a fork in pretty easily a fair way down, so the soil does fix itself over time as the soil health improves. Are you seeing much soil life (worms and multi-legged beasties) in there?
I'm not so familiar with your climate conditions (being UK-based), so some of my essential edibles might not work so well. I love rocket (arugula), and it self-seeds like a champion, but that might bolt very fast in your summer? Over here, comfrey is a favourite: edible (though to be honest I rarely eat it), a good insect plant, and has amazing long
roots that pull nutrients up from a long way down in the soil. It is pretty heat- and drought-tolerant over here so might be good?
How about some fruit or nut trees? Give a bit of shade in hot conditions which can be good for both humans and other plants...
Annoyingly I don't have a proper 'before' photo for my garden, but this album has a couple of photos from 8 months - 2 years in. (It's 3.5 years now; need more photos!) In one of them you can see next door's fully-paved garden, so my 'before' photo basically looked like that!
https://www.flickr.com/photos/julietkemp/sets/72157650736608751/
(edit: aha, partner has come good with a photo from the month before we actually moved in. Only greenery was a single
rose tree!)