So, my original guess was since Watch Dogs is an old game, they are probably doing something that breaks the PS5's suspend feature.
A quick search online shows that other people have the issue too.
- One case suggests quitting to main menu and then going to rest mode works. Not the best solution since you have to save and quite the game, but at least you don't have to load the game again.
- Another site mentions that it was working with Watch Dogs, but then they started Assassin's Creed Unity, which has issue with this feature, and after that Watch Dogs has stopped suspending too. No idea why Unity has the issue though, but that could be back to my original point. Old game, with some feature / bug breaking the feature.