If the tilth of the soil is good, and you’ve eliminated the competition in the form of weeds, and (I presume) you have a good handle on meeting the light and temperature requirements of annuals in your climate … then it’s time to think about nutrients. Nice succulent, fleshy, fast growing annuals are nitrogen hogs. You’ve added a ton of carbon to the soil, but both straw and wood have notoriously poor nitrogen content. So I agree with Hamilton Beltchman — compost may help. Manure compost, or vegetable/comfrey compost, or worm bin castings made with kitchen scraps, or aerated compost tea sprayed on specific plants that need a boost. Pee in the pile. Scrape any little weeds that pop up in garden with a hoe and let them die on the surface next to your plantings. Mulch with fresh cut green grass/pasture (before the seed heads!)
From the standpoint of the microbiome of the soil, I think of it this way: The majority of plants prefer to live in soil made up of other plants that occupy the same ecological niche as themselves. That’s what they’re adapted to, and that’s the microbial community they will respond to best. Hardwood fruit trees, for instance, “like” ramial wood chips and leaves. It’s the soil of a hardwood forest, sped along. Conifers and acidic bog plants such as vacciniums are fond of conifer chips. And fleshy annuals, the denizens of early succession and disturbed ground, like soils where a lot of other herbacious plants have lived and died. They are a bit grudgy against wood and all the fungal associations with wood, because the forest is not kale’s natural habitat. Unfortunately, grass pretty much loves exactly the same environment as herbacious annuals. Perennial grasses are the next ecological stage after the annuals, and they absolutely know it, as much as plants know anything. So battling grass tends to be ongoing.
What I do is this: I’ve established beds that I think of as enriched annual islands among the various perennial plants. Compost, leaves, grass clippings and wood ash go into the islands, but not too much wood or needles/forest duff. Even in a hugel pile, it has worked best to have the wood fairly buried under a lot of herbacious materials. Wood chips I use on the paths around the islands and around various trees ands shrubs. Chips do help establish a grass-free perimeter, so there is less grass invasion into the tempting beds. But the annuals are happier to have the wood degrading off to the side instead of right in their immediate root growing zone.