Since “zebra” is a remote branch, I was thinking I don’t have its data
locally.
You are correct that you don’t have the right data, but tried to resolve it in the wrong way. To collect data locally from a remote source, you need to use git fetch. When you did git checkout zebra you switched to whatever the state of that branch was the last time you fetched. So fetch from the remote first:
# fetch just the one remote
git fetch <remote>
# or fetch from all remotes
git fetch --all
# make sure you're back on the branch you want to cherry-pick to
git cherry-pick xyz