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”.
Sounds like a job for a rasberry pi with pihole installed: https://pi-hole.net/
I’ve really wanted to start tinkering with rasberry pi, so maybe that’ll be a fun first project!