Here is an answer from our Iowa State University Extension and Outreach horticulture specialist.

I suspect there are two potential issues occurring with your vegetable garden. Either one of these issues could be the culprit or it could be both.

First, since you are not sure what material was used to create this “compost” pile or what material was put in this area, there cold be herbicide or other plant growth inhibitors in the soil. Plants such as tomatoes, peppers, and beans tend to be more sensitive to these compounds than plants like onions. These compounds could be herbicides introduced through things like lawn clippings or compounds from other plants like black walnut that are composted in this area. Typically, as long as these compounds are not continuously applied to the area, they will leach out or break down and the plants will grow out of the damage.

Second the soil in this area could have low fertility. Plants like tomatoes, peppers, and beans benefit from more nutrients in the soil from things like fertilizers or compost than plants like onions, asparagus, and kale. Consider applying fertilizers to the plants to see if that can help them grow out of this damage. Use a general purpose, balanced fertilizers as instructed on the label.

Regardless of what the cause is, there would be great benefit to conducting a soil test. This soil test will likely be able to tell you about the fertility and give you a good place to start from in improving the situation for your vegetables. Iowa State University no longer provides soil testing services. However, soil testing services are provided by neighboring universities and private laboratories. Examples are listed below:

University of Minnesota soil testing website for lawn and garden - http://soiltest.cfans.umn.edu/testing-services/lawn-garden
University of Wisconsin soil testing website for lawn and garden - https://uwlab.soils.wisc.edu/soil-samples/lawn-garden/
Waypoint Analytical - https://www.waypointanalytical.com/HomeOwners
AgSource - https://www.agsourcelaboratories.com/lawn-garden-testing-services