I compressed my 2.2.0 backup to 644 MB using 7-Zip (LZMA2, Ultra). WinRAR says it's 2% of the original filesize. I only finished Zelda: BotW on the thing (played from the cartridge) and reached the 1000 screenshot limit once. That's it. If you backed up a newer firmware, Nintendo may have added extra files and stuff, but definitely not something that would break 1 GB, imo. And the save game files can't be that big.
The backups initially take up 29.1 GB space because that's the size of the internal memory (the NAND chip). It's encrypted, so it backs up the whole thing because if/when you decide to restore that backup it will put the data blocks in their original order. And even though they are encrypted, the blocks of memory containing free space are compressed better, because each free space block is similar to the next. The compression software looks at the data and says "yeah, 98% of these blocks are similar, so I might as well keep one intact and duplicate it 97 more times when it's decompressed".
If your backup takes up 12 GB AFTER compression, that means it had a shit ton of stuff on it.
But I suppose you could mount the internal memory as a mass storage device with TegraRcmGUI and use something like CCleaner's "Drive Wiper" (Free Space Only - 1 Pass) to zero out the free space prior to making the NAND backup.