Q.My tomatoes/cucumbers burned in my garden
My tomatoes/cucumbers burned in my garden overloaded with rabbit manure. From Oct. until March, I was placing fresh rabbit manure (mixed with hay) on the top of my garden soil. Late May I planted tomatoes and cucumbers (at the same places where they produced plenty of excellent veggies last summer without any fertilizers). The soil looked very healthy, like a chocolate crumbly cake with lots of worms. In a week my plants died (turned yellow, then light brown, then looked dried, also the soil was wet). How can I amend my soil to plant new cucumbers this season? If I dig some top soil into it, will it work?

I do agree that the rabbit manure was most likely still to hot for the tender vegetable seedlings.
You are not alone as this is a common issue.
Wet soil could also be a factor in your plants failing in the garden.
They need well draining soil and sitting in soggy soil will kill your young plants.
I learned a formula many years ago that I try to remember when amending my garden beds (or starting a new one)
45 % soil that is on the ground
5 % organic material/compost
25 % water
25 % air
5 % luck
I would remove some of the compost, then add top soil.
Try to keep the compost away from the new plantings and keep the compost to the edges.
If the soil is still feeling heavy add some peat moss to lighten it up and provide good drainage.
You mentioned lots of worms, let them get to work.
Best of luck.
https://www.gardeningknowhow.com/composting/manures/rabbit-manure-compost.htm