I have just downloaded BF6 RedSec on the EA App and can confirm the reward was there for me to claim under previous messages section, only the deployment for me. There was a lead the way pack but it kept getting me to purchase.
Pretty stupid download too, it downloaded 75GB, then HD Texture pack for 25GB, then another 8.9GB of Redsec Addon, then some other HD texture pack for 20GB before it was done, this was by far the dumber than the COD (Please reload the game to apply the update when you've done the game update)
I purchased and play through Steam, both my accounts are linked correctly, I just checked and also in game it shows, there is an issue with the linked account though I feel, when I invite a friend, it sends it via EA app, not Steam even though I am on Steam, it could be the other way around, I am not sure but pretty sure friends notice the same thing.