I have both sparse bundle & backup bundle. Can I delete one?

The backupbundle was created when you moved up to the Catalina 10.15.x operating system. The sparsebundle was used on previous operating systems.

Delete the sparsebundle if you need more space, keeping in mind that your backup history will likely not go back any further than the date that you installed Catalina on the Mac.

I would recommend using a USB drive to archive the TC now.. you will need a drive of equal size to the TC so 2 or 3 TB or greater.. formatted Mac OS extended journaled .. It will take a day or so to archive.. option is in disk tab in airport utility.

Once that is accomplished erase the TC drive and start a new backup.. this seems to be a big help with Catalina which is fragile enough anyway.

Does that mean the backup bundle currently has my whole hard drive? The sparse bundle would just include anything that I had deleted before Catalina?

The whole disk will be backed up in the backupbundle .. the sparsebundle has your previous OS backup and history back to when you started that particular backup.

Everything on your Mac was backed up to the backupbundle when you installed Catalina. So, if you installed Catalina on January 1, for example, the history of the backups on your Mac will go back to January 1.

If you delete the sparsebundle, everything prior to January 1 will be deleted.

If you want to be super safe and keep a record of everything, LaPastenague has a great recommendation for you. Chances are, a few months from now you will decide that you really don't need all the old backups and you can erase the USB drive and use it as a spare. Or, Archive the existing backupbundle at the time......in case the Time Capsule hard drive fails.....you still have a backup on the USB drive.

Another way to say the same thing.......one backup may not be safe enough, because hard drives do fail.