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Whoops, I'm sorry, this has been implemented only for version 17.1 Preview: here you will have Local|Stash Selection

This has been implemented for version 17.1 preview. Either way, thanks for pointing out to new "git stash push" functionality -- we should probably use this command instead of our own file-selection stashing (SG-10926).

What exactly do you need?

By splitting up into separate options, it's easier to describe and understand. You may remove both buttons from the toolbar, if you prefer.

This behavior is expected, "git status" will display the same modifications. After copying files you should invoke Local|Reset, option Hard. Be sure everything has actually been committed before copying!