Starfield not starting on my PS5 PRO - has anyone had similar case?

I was quite excited to get the Starfield on PS5 and preordered a physical copy which arrived yesterday. The problem is that I installed the game and it turns out only a part of it is on the blu ray and about 1/3rd still needs to be downloaded which kind of beats the purpose of collecting the blu rays in this case. Ok, whatever I can live with this disappointment when I have some relaxing time with the game. But it turns out not to be possible because the game won't start. I am logged into playstation network, can normally browse ps store, but when I start Starfield it says "you must connect to internet to update Starfield", and the game won't start. I tried updating the game from the ps5 menu, but it's the latest version. Has anyone had similar issue and was able to solve it? I am really hoping it's some dumb thing I have not set or done and not another quality error from the company.