However, my understanding is that using 'prune mode' shouldn't affect the wallet's available balance, as Bitcoin Core still has to go through and verify every historical transaction.
That is correct.
Could it be that the majority of the ~12BTC is caught somewhere in the past, and has actually been spent in 2012-2014 (by me), but for some reason the client thinks it's still available in 2021? How odd...
This is unlikely because bitcoin core is wise enough to check and update your wallet information as it continues syncing. But let's see what others think who are more familiar with bitcoin core, I'm not the best at it.