If you used bagged potting soil it's possible that it is contaminated. Three summers ago I got a truck load of composted manure/hay from a big horse farm and applied it to a new garden spot. I also put some in a separate tomato bed at my neighbor's house. The plants in both locations ended up looking exactly like your blackberry leaves. At first I thought it was a water issue, then some kind of tomato blight, but I had a nagging feeling it was the horse compost. My neighbor ended up pulling out all of her tomatoes.
I didn't plant anything there last year and just let it sit fallow, but this year I did plant, hoping that whatever was there had broken down. I was wrong. The tomatoes are struggling with the same severely upward curling leaves, though they are better than the first year and are setting fruit. Now I suspect that the
hay from the horse farm was sprayed with Grazon, a broadleaf herbicide that is wreaking havoc on gardens everywhere and showing up in purchased bagged soil. I hope that's not the case for you and that it's just some blight, but I heard someone say that leaves curled downward is disease and leaves curled up means chemical damage. I don't know if that's true.
There have been many rants about it on YouTube for the last few weeks and I'll link one. What a mess!
https://www.youtube.com/watch?v=w8oL1E-JP1s&t=211s