Wow, this is awful. Some people reported that these ads are also very petty and not necessarily related to the game, like apparently Elden Ring shows an ad for a licensed mousepad when you hover over the game now…
Edit: Playstation Product Manager says this is actually a new bug. I really doubt it but they do seem to be “fixing it”.
While it defaults to a console-like experience it is meant to be altered, they give you a full desktop environment as standard and even provide instructions to install Windows if you really want.