(AFAIK there's no mass-discard option, but I've never really thought about it before because 99% of the time Preview is showing me something that's already on disk)
Yes, screenshot part of the screen, do a quick edit or highlight in Preview, and paste it to GitHub or email. I never want the screenshots to be saved to disk but end up with my Preview full of "dirty" screenshots.
There used to be command key shortcuts for the don't save/cancel/save (command-d/s/c iirc?) dialog buttons, but they've changed the ui to delete/save and seem to have removed the keyboard equivalents.
The right way to do it (in my opinion) would be option-click on the Delete button or command-option-D, but they don't seem to have implemented that.
Command-d is still mapped to don't save (at least in Preview, just verified). Escape is cancel.
Are you running macOS Monterey? It doesn't seem to have a Don't Save option in the "Do you want to keep this new document" dialog box - it's Delete, and command-d does not work for me.