Thanks for the experienced advice, by the grace of God.
Composite image, top and side.

I don’t know if this is true or not, and I don’t know what you have growing there, but I was told recently that if the stem is woody to dip it into rooting hormone powder, and you have a chance.
My Picture This app says it a Japanese Euonymus.
I need some more detail on what it actually IS before I can tell you how to propagate it.
Is it a shrub? Is the stem ‘woody?’ or is it some sort of perennial that I’m not familiar with?
Is it a variety of Euonymus? A landscape shrub?
https://gardenerspath.com/plants/ornamentals/best-euonymus-types/
Beautiful plant - and most transplanting like that is experimentation - give and take and it may take several tries before it works.
I know that to be a hardy plant so it should take - maybe plant one cutting in potting soil, another in water and see how they do. Or do several. I’ve done this with many plants and usually one or more “takes.”
Ditto for grafting. I’ve seen grafted plumerias that were beautiful, different colored blooms on every branch. I asked one gardener how he did it and he told me he grafts many many branches and usually only one or two take.
That’s one of the beauties of gardening, it’s very fluid and flexible - and we are also beholden to the weather, which changes year to year (my figs this year are very very small, I think from us having an extra cool spring, they didn’t get the heat they need to ripen and plump up properly)