You can drag edges, but it doesn't seem to have a concept of a "square" beyond the tool itself. So after you've placed it, you can't move individual shapes around. The select works more like a text-editor's highlighter than something like the lasso tool in draw.io
It does, but that selects and moves the cells not the objects and then redraws the cells? Actually, going back to have a play I see that it does allow some modification of existing objects but it isn't terribly flexible.
I've just done a quick search and found one that I've not spotted before, which is a bit closer to what I want in that one respect, but not nearly complete overall (and not seen a check-in in 8 years): https://textik.com/ - that might illustrate the key difference that I see missing in asciiflow.
If i understand you, the Mac-only Monodraw handles this fine. It lets you draw objects, point to objects (say like a diagram), and then move them around with the pointers auto adjusting to remain correct.