If you’re growing climbing beans you could do Three Sisters! Idk whether it aerates the soil, but it’s a well-proven companion planting schema that makes excellent use of the space and reduces the work needed to grow
If you’re finding that the soil is getting too compacted, you can try planting a green manure mix over the winter - that’s a number of cover crops that improve the soil by breaking it up, fixing nitrogen, preventing erosion, and so on while you’re not growing anything there. I know people grow daikon radishes for this reason too, since their root penetrates really deep (daikon literally means “big root”) and so they’re grown over the winter and then left to decompose
Alternatively, you could mulch the soil heavily in the winter with something like hay, which will leave a freshly composted layer of rich, loose soil at the top while contributing nutrients further down as well. Tons of people leave used hay bales on their curb after Halloween for trash pickup, which is perfect for overwinter mulching if you just look around local neighborhoods to grab some. Three Sisters produces a lot of unused plant matter though, so you might not even need to get any!