I spray herbicides for weed control. After all I worked in Weed Science for over 35 years and sprayed my share of research plots. Many herbicides have longer than expected life in Idaho. I expect herbicide carryover from compost and few vegetables are immune to damage. Composting is a necessary part of gardening in Palouse clay soil so it needs to be managed to reduce injury from herbicide residues.
To test for herbicide residue in the soil use bean seeds planted in a pot of soil from the garden. If leaf is cupped or curled the soil has herbicide is present.
Thoughts and hacks.
Set aside a low spray area and harvest grass clippings from this area for mulch and compost. Spot spray with a short residual herbicide when you need to spray in the no spray area.
Split garden into two columns or strips. My strips are used alternately to grow snow peas/nitrogen fixing green manure crop and the other vegetables. This rotates the crop to reduce disease. Dig compost into 25% of pea strip but do not plant peas into it (fallow).
Plant tomatoes and other super sensitive crops in the space of the other vegetable strip that will have compost dug in the next year. Plant carrots in the area that received compost last year. This rotation allows eight years before planting sensitive crops into a composted area that may have some residual herbicide.