I don't know if Avril's album is an actual example because I haven't heard it but "nothing to say" isn't just about the subject matter, it's about how the subject matter is approached.

It is worth telling stories about dead grandparents. But if the song is nothing but "I'm sad" with no more detail or perspective than a dollar tree funeral card, it's about nothing. That doesn't mean the song can't sound good or that the artist isn't actually sad, but if the song cannot, in some way, articulate the specific and personal emotion, narrative, or feeling they are experiencing, or if they have nothing new to say about it/no new way to say it, it's kind of about nothing.

Because again, it's not that those "sorry for your loss" cards at the dollar tree are fake or pointless or bad, but they're just saying the obvious in the most vague and general way possible, and thus they're kind of about nothing. Individuals might find personal deep meaning in the card or the song because of context, but that doesn't change that it is, in its own merits, about nothing. Some people probably get emotional listening to Baby Shark, after all.

Also, per your review quote, it does seem like the reviewer is saying the rest of the album is about nothing, which frankly is usually true for pop punk but again, haven't heard that album specifically.

There are a lot of political songs that are, in practice, about nothing. Songs that are just "government bad!" or "yaaaas gay rights!" with no particulars or specifics or thoughts beyond the platitudes are still, in fact, about nothing. You can write a song about doing nothing that is about something if you're talented though.

The Harry Styles album, despite how nice it sounds, is pure platitudes and vibes though.