Will updating Storage Studio affect my moved files and settings?
Short answer: No. An update replaces only the app; your moved items, shortcuts, rules, accounts and settings carry over. If macOS drops Full Disk Access after the update, Storage Studio tells you and switching it off and on restores it.
No. Updating replaces the app itself; your moved apps and folders, the shortcuts left behind, your rules, accounts and settings all stay as they are, and the new version picks up where the old one left off.
One thing to check after a big update: macOS sometimes drops Full Disk Access for an updated app even though the switch still looks on. Storage Studio will tell you if that happens — turn it off and on again in System Settings → Privacy & Security → Full Disk Access to restore it.