You are confusing the process of going from entropy to a seed phrase (which is what you are talking about), and the process of going from a seed phrase to a private key (what OP is talking about).

As you've quoted, you take the SHA256 hash of your entropy to generate a checksum, which is appended to the entropy before the resulting number is used to generate a seed phrase. However, once you have the seed phrase as in OPs case, you don't use SHA256 in the generation of private keys, but rather HMAC-SHA512. Using SHA256 on a seed phrase is essentially creating a brain wallet, as nc50lc has said above.