You can take the backup of Zephyr Squad data to restore later if you subscribe again to Squad. Data stored in Jira like test cases and test cases attachments are not part of Zephyr Squad backup. To back up the test cases, you should take Jira backup.
The data in Zephyr Squad will be available for six months and you can access it only when you install Zephyr Squad and subscribe to it.
If you choose the upgrade with test cases only, there is no possibility to transfer the data (test cycles and test executions with the upgrade engine later once the mechanism to transfer data is available.
During the upgrade, the Jira settings and permission remain the same. You can find the migrating fields and their respective mapping details on the Data Transfer page.