What plant would you plant? I heard good things about Dichondra but unfortunately it doesn’t survive winter freezing / snowing.

That depends on where you live, you should plant native species. I would go to my local botanical garden and ask them what they have on their meadows. If you don't have a botanical garden around, a local university might have information, eg https://extension.umd.edu/hgic/topics/lawn-alternatives

In my area, they hold native plant sales through the local conservation district. Here is an example: https://kingcd.org/programs/better-backyards/native-bareroot...

I've purchased native trees, scrubs and native flower mixes through them. They seem to be held only once a year but the prices are very reasonable.

You could get a native wildflower mix, and seed bomb with that. After a few years, it’ll settle into patches that of species appropriate for the sun/shade level, and look more natural. It’ll make the native pollinators and birds happy too.

Sure, but then I might as well plant salad, rosemary etc (i.e. actually useful plants... along with some species that maintain / improve soil nutrition). In my view, the main purpose of ground cover is to be able to walk on it...