You'll have to kill the grass first in order to not have it take over again, the flowers soon die out. With environmental conditions present here tending greatly to favor the prevailing of grasses over flowers - all the more so because of all the weedy Eurasian grasses that are around. So that even in the minority of local sites such as bedrock outcroppings and certain other naturally treeless locations where shallow or dry soils have allowed the persistence of numbers of native meadow flowers invasion by weedy grasses and other threats is often occurring. As it happens I did a garden consultation this year in Skagit County, Washington where the client had had the same idea as you. The wildflowers had been planted and were flowering in the part of the field where the septic was. Vigorous grasses were present all around the planted section, I don't remember what the preparation method was but it certainly looked like the scheme was not going to last unless periodically redone. Also the "northwest wildflowers" were all kinds like might be seen growing natively in the Siskiyou-Klamath area or even farther south in California; at least they weren't the various Old World species typical of wildflower mixes offered and planted in our region. But the point remains that checking to see which particular species a mix being considered contains is an important aspect. At least where a body is trying to support the local ecology, as you apparently are.

Vernonia baldwinii Vernonieae, Chicorioideae, Asteraceae, Asterales https://www.illinoiswildflowers.info/prairie/plantx/baldwin_ironweedx.htm#:~:text=The%20alternate%20leaves%20are%20up,or%20sessile%20against%20the%20stem.

It doesn't look like a wildflower and may not even be from this mix You are correct - it is a woody plant, with the specimen shown predating October. And if you are located in North America: This aggressive grower poses a threat to native plants and communities. Its vigorous growth forms mats of monotypic evergreen groundcover that displaces and excludes most other plants, including native wildflowers. Extensive infestations can be found under forest canopies. https://www.invasive.org/weedcd/pdfs/wow/common-periwinkle.pdf

Picking up all the bigger sticks and branches in a natural woodland garden makes a major difference in the look and feel of the space. It is for pretty much the same reason you wouldn't leave all the deadfall from large mature trees in a more convential garden. All those sticks and branches fall in and on top of your plants. They also decompose much more slowly than leaves and can pile up quite a bit over time. The plants matter just as much in a woodland garden as any other garden. You don't want them buried in and fighting to come up through a bunch of sticks. It is the same reason I want to have all the remaining dried bits of the herbaceous perennials chopped down before early spring. The biggest bloom in a good east coast woodland garden is in the early spring. The majority of the native spring ephemeral wildflowers are less than a foot tall. You don't want the visual competition of a bunch of taller standing sticks with shorter plants. Bottom line is that keeping the forest tidy is to display the plants you and nature are growing to their best advantage.