On sourcetree, how can I recover stashes after checkout on a different branch?

Welcome to Stack Overflow :)

Stashes are indeed listed in the sidebar, but in your image they're collapsed. The 'Show' links next to Tags, Remotes, Stashes, etc only show on hover.

Note that trying to apply a stash from one branch to another branch may result in conflicts to resolve. In this case, sourcetree will not delete your stash automatically, as it would usually, rather you'll need to right click and 'delete' stashes once you've successfully applied them.