Hi,
To keep custom modules and Studio customizations in staging while restoring only production data, you should restore the production database without overwriting custom modules. This means you either:
Restore only the data (not the filestore or custom modules) from production into staging.
Or restore the full production DB, then re-install/merge your staging custom modules and Studio customizations back.
The key idea is to separate code/customizations (kept in staging) from data (copied from production).
Hope it helps