I'm not an expert, honestly, @systlin will probably know more than me, but here's what I've learned over the years, and from slowly replacing our lawn.
Bear in mind, a lot of this will depend on your local climate and you should always research your own local area first.
My dad grew all our fruit and vegetables when I was a kid, and he'd routinely be out back replenishing the lot with manure fertilizer (a lot of manure fertilizers need to be matured, you can't just shovel cow shit onto your lawn) and giving the garden time to rest in between growing things. He also swore by vermicomposting, or worm composting. To this day, the soil in their backyard is pitch black and grows monster-sized produce. Their "grass" is also mostly clover and moss, which requires minimal maintenance and works well for their damp climate.
Something else I've since learned is to make mulch out of fallen leaves. If you live in a drier climate, you can let the leaves that fall from your local trees dry out, then chop them up (we run over them with the lawn mower) then spread it out over your yard.
If you live in wetter climes, or you just like to compost things, throwing leaves into your compost mulch is a great way of returning vital nutrients and minerals into the soil that are otherwise depleted as well.
We're also replacing our lawn with clover, which requires less mowing, less watering, and doesn't require fertilizing because it actively replaces nitrogen levels in the soil.
It's great for pollination and also good for local wildlife to munch on (we have so many bunnies) and, as I mentioned above, also helps balance nitrogen in the soil, which can often be stripped away by "traditional" lawns. You also don't have to aerate it because the root structure leaves behind macropores in the soil, which is heaven for our little worm friends who do a fantastic job of keeping soil healthy.
Clover is obviously not best suited to everywhere.
It really does depend on your climate and where you are in the world, but it can be a good place for many people to start moving away from lawn culture and help to replenish some nutrients in the soil in the meantime.
Avoiding pesticides and herbicides is also good, as is researching what used to grow where you are now, and trying to find some native pollinators. I've seen a lot of people here planting native prairie flowers, and it's really heartening to see how well they thrive after a few years.
Also avoid tilling where you can. We now know it breaks up vital root structures. This is more important for farmers, but it doesn't hurt for us to do either.