Every fall, top dress your garden beds with compost. There’s no need to dig it in, just spread a couple inches on top of your existing soil and let nature do its thing.
This restores nutrients and also adds volume, as a little soil is lost every time you pull out plants.
Compost on its own is an effective mulch, but your yard is probably full of free organic mulch in autumn that you might as well use!
Fallen leaves (preferably shredded, if they’re large and thick), pine needles, grass clippings, twigs and small branches, even annual weeds that haven’t gone to seed all make fine mulch material.
There’s a cover crop for solving nearly any problem, whether you want to break up hard soil, replenish lost nutrients, or reduce soil-dwelling pests.