Assume you are already given a properly-salted, password hash $X$ from some slow PBKDF (e.g., like Argon2id).
Now, you want to apply some large (~256-bit) secret "pepper" $S$ to it before storing it in the database.
Is there a significant difference between storing it as an $$\text{HMAC}\left(S,X\right)$$ (where $S$ is the secret key to the HMAC of $X$) versus a "much simpler/basic" $$H\left(S\mathbin\parallel X\right)$$
where $H$ is just some SHA-2? (e.g., SHA-256/512)