So many ways to make a small garden look wonderful. But lots of pots, plants in different sizes, multiple climbers etc and fill it up is the trick. It does have a cost and can be time consuming but this is manageable in many ways, from using old receptacles as planters, to adding cheaper plants like strawberries or bamboo, but way less cost and work than what you’re suggesting. Which is not just dig the patio up and chuck some wild flower seed down. It’s much easier to do pots and plants. And you can do bits each year and build it up .
that’s what we have done on our patio. Each year we add more to it. Repot where appropriate, it’s not much work on an ongoing basis.
we have surrounded it with climbing roses, large bamboo in pots, acers, ornamental grasses, camellias, palms, jasmine, honeysuckle, clematis , Cordylines, etc and then lots of small perennial plants, and each year we plant in some cheap annuals, like petunias etc. and it’s wonderful. We have spent about 200 to 300 a year for the last 6 or 7 years on plants, soil and pots, and now it’s stunning.
here is an image of a small garden with a similar theme. As said, unless you’re a keen gardener wanting to manage this properly and some deep pockets, I’d steer clear of digging your patio up to turn it into a meadow.