Carolina jessamine is evergreen but I'm not sure how drought tolerant it is.

Carlolina jessamine grows wild all over the South.
It is as drought tolerant as any plant in South Carolina.
I LOL every time I see it in pot at big box stores.
I have it on many a rusty fences on my ten acres,& I would help you dig it, too.
The leave are poisonous, like many plant including tomato vines, so do not let babies crawl around it.