Using a bit long enough to reach all the way through timbers slowly drill until you feel bit break out hidden side,make bit,withdraw and measure remaining wood that isn't rotted.

What is a ”walk up”?

What material composes the foundation of your house? (I take it the second photo is an inspiration and you don't have that stone foundation.) If it's brick, you could try to match that. Here in Maine (similar clime to yours, probably) we had success rebuilding a 4' retaining wall out of vintage brick; we love the color against the green of various plantings, doesn't rot, and you can design a pattern that locks them into one another. Has held steady for over 7 years since building it, although it's all so location-dependent of course.

I love the idea of making that area into a raised enclosed atrium if you can swing it; I'd imagine you could get a lot more useful function out of that than the open sunken patio. There would probably be an inevitable trade-off of darkening the basement at least a bit, though -- do you have a larger photo with the entire back half of the house?

Hopefully someone here can give some input on how to negotiate a new enclosure -- make it two level, maybe? -- without losing too much of your light.

We are near Minneapolis. Hot, humid, buggy summers, cold unyielding winters. It’s so weedy and overgrown back here, it’s embarrassing. Our foundation is thick poured concrete, but our soil is dense clay, so anything else is at its mercy. We have a new window in the kitchen that would be an obstacle if we did one of those curved glass two-story sunrooms, but I think there’s room below them to attach it. It’s only vinyl siding, so it wouldn’t be complicated to tie it into the house there. I’m leaning toward putting walls on proper footings, even if we didn’t enclose it now, we would have that option. Perhaps just more poured concrete. We could clad it inside with brick or tile.

Update!

While building it as an enclosed attrium was a budget buster, we did finally have the walls and steps replaced with cement blocks. it turned out spectacularly! No more smelly creosote. We were unable to go all the way back to that window, but we did push it back and gained a couple feet. the steps are big slab concrete steps and well-worth the splurge. the soil here would have distorted them in no time if we had used small pavers. I need to landscape it to add a bit of a saftey zone above that wall. (that‘s not a shadow - it’s wet from watering the grass seed as the lawn needed to be restored.)