So they generated private keys using a simple k = k + 1 scheme.
You don't understand how key derivation in BIP32 works and your foolish assumptions that puzzle keys have any dependency from one to another is deeply flawed.
Even though key derivation in deterministic wallets is deterministic, it doesn't mean that you can calculate a sequential key solely from knowledge of its predecessor or successor (or any other key).
In a deterministic wallet all keys appear as if they're random. Period! There is no exploitable relation between individual keys. Masking them down to a certain bitlength doesn't introduce any new relation.
But you can happily continue to read tea leaves...
I dont say any direct connection or dependency between them.
I mean some kind of statistical prefix frequency similiarity among huge keyspace around them maybe 😅. I just persue to look it deeper. As i scan lots of statistical bias in several prefix count / frequency in dissected private key keyspace result