How can I change the default location Snipping Tool auto-saves screenshots to?

When you open the Windows Snipping Tool using +Shift+S, it will autosave the images to %UserProfile%\Pictures\Screenshots, but I want to change that default location.

How can I change the default save location for the snipping tool only, and not anything else?

• There's a ton of threads about this on Microsoft forums, but none actually offer a solution:
  • How to change the Snipping Tool autosave location? [sic]
  • Change Snipping Tool save location on Windows 11 22H2? [sic]
  • How can I change the default folder that snipping tool uses to save images?