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”.
Package manager choice is pretty important, and for that I always recommend debian-based for a pc for a new Linux user. APT is just so good.