That isn't necessarily the mental state of HN. Given the nature of HN, it could just reflect interest in the subject.

The way this is worded, it seems like the author simply counted the number of posts with negative words in them. And then compared the number to last year.

In that case, the increase could be explained by more posts on HN overall. Without any change in "mental state".

Lets have a look into the calculations ...

Hmm.. as far as I can see, the calculations indeed do not take overall change in posts into account.

HN didn't have a significant increase in traffic due to covid compared to other sites, hence the more submissions didn't lead to more traffic. OP dropped also submissions that didn't hit the frontpage by removing those with less than 10 comments. So the 19% more submissions couldn't influence the result. And even if, you'd still have 19% vs 40%.

I don't see how other sites play a role in this.

Only counting posts with 10+ posts does not guarantee that the baseline is the same for the two groups. You seem to imply that the number of posts that reach over 10 points means they reach the frontpage and that the number of posts that reach the frontpage is always the same during two time periods of the same length. But I don't see how either of these two assumptions has to be true.

The problem with the "19% vs 40%" comparison is that it does not compare the same thing. According to this article:

19% is the increase in total posts

40% is the increase after posts with less then 10 votes have been removed AND posts without the negative keywords have been removed.

This comparison is not the right one. Either posts with less then 10 votes need to be subtracted from both groups or from none of them.

Relative to what? How did the dataset have those "in_lockdown" differenciation?