Does hashing PII in logs provide any real security?
Will this setup provide any real security if the logs are leaked?

One issue is the fixed salt.  With that, the translation of email to hash is fixed; that is, if the attacker sees two identical hashes, he knows that they were the same email address; he might not know what the email address is, but he knows that the two emails were to/from the same person.  And conversely, if the hashes were different, then they referred to two different email addresses.
One possibility would be to include a 'per-hash' salt (salt1), which is randomly selected each time you generate a hash [1], and so the email address would be replaced by salt1 + sha3-256( salt + salt1 + email ) (where + is string concatenation).

[1]: You could generate the per-hash salt sequentially if the order you generated the hashes didn't need to be secret; this would allow the per-hash salt to be shorter without worrying about duplications.