I'm wondering if the problem isn't one of expectations rather than the tires.

Switching to snows or studded snows makes most cars feel invincible in the conditions the OP describes. They make bad conditions feel like clean dry pavement, and give a feeling of enhanced stability.

That's never going to be the case with bicycles, mainly due to the weight. No tire isn't going change the fact that compressed snow can throw my bike around. In snow that's been compressed by a two-ton vehicle, there's not much my weight (one-twentieth of the vehicle's) is going to do about it. Instead, the surface will do to me. The best I can hope for is a tire that will make the most of what traction is available so I can stay upright.

In loose snow and slush, there's enough give to the snow/slush and weight for my bike to sink to the pavement. There I can enjoy enhanced stability and a near dry-pavement sense of control. On bare ice, the studs can do their job. It's the in-between where my insufficient weight is the issue. No tire will change that. Or at least, no tire I'm capable of pedaling.

Yes, lower pressure helps. It helps a lot. But it is not a panacea. It helps only to the extent that the tire can mold itself around smaller surface defects rather than be pushed around by them. Larger surface irregularities still push me around.