No differently to the previous way of doing stacked PRs? There's no getting around the fact that you're force-pushing a new version of each branch in the stack.
This just automates the previously-manual process of checking out branch2 and rebasing it to point to branch1, instead of pointing to the commit that branch1 referenced pre-rebase.
I usually just `git rebase --onto` any dependent branches. I will have to see if `--update-refs` is more convenient (it should be) and if it works well enough for me.