In Smart Planner, you can create and restore backups free of charge from "Google Drive backup" in the settings screen (you can also open it from "Backup" in the menu at the top left of the screen). Tap "Login with Google" and log in to the Google Account you want to save the backup to before using it.
Google Drive backup is not automatic syncing. It never runs on its own. You back up the data inside the app (events in the Local calendar, ToDos, notes, and diary entries) to your own Google Drive manually.
If you use the same Google Account, you can also share data with your other Android devices, such as a tablet. Both devices refer to the same backup data, so if you tap "Create Backup" (or "Overwrite Backup" for subsequent backups) on your phone and then "Restore From Backup" on your tablet, your phone's data is transferred to the tablet. You need to tap overwrite and restore manually each time, but this lets you share data across multiple devices.
※ Events saved in Google Calendar are stored in your Google Account, so they are not included in this backup (they appear on your other devices once you register the same Google Account).