A bug report and a question about Premium Purchases

[ScawyKaim]

So, after completing the Union process, I logged into my ps4 account on my PC, and since then I have been spammed by an Inbox notification, that always forcefully opens the Inbox, only to show nothing new, it does that after logging in, and after every mission I do, and no matter how many times I open it or go through the messages, it has not disapeared. I don't really mind it, just wanted to see if anyone else has had this thingy happening to them.

But now, about the question I wanted to ask. I am a PS4 Tenno and have gone through the Union process, I wanted to know about how do Premium puchases work after Cross-Save, can I now buy stuff directly from my steam account and still get the Prime Access and/or 10 Year Aniversary stuff on PS4? (Not talking about tennogen, that I know is platform locked) It all indicates that yes, but I wanted to be sure just so I don't throw away 140BRL to the Void.
If anyone could answer me this it would be of great help, really wanted to buy the 10 Year Aniversary pack, but on the PS Store it is way too expensive over here, buying it on Steam (with localized pricing) would be the only way for me to get it.