I can read that you have used the same email for your SHIFT account and your PSN account, but have you actually linked both accounts together on the SHIFT website?
You can only redeem the codes in-game if both accounts are linked.
I did find an entry on the official 2K support that explains how to link the PSN account to the SHIFT account for Tiny Tina's Wonderland and I assume that it works the same way for Borderlands 2.
Official 2K Support Website Link: [TINY TINA'S WONDERLANDS] SHIFT ACCOUNTS AND YOU
In the past Borderlands 2 had issues with SHIFT codes on PS3 consoles when you linked the accounts via the website. If that still happens for you on the PS5 the solution was in the past to delete the existing link and to re-link the accounts, but this time you start the process from the PS5 and not the website.