No, as your own article points out, there’s a correlation between gun ownership and GUN suicide rate, yes, but not suicide rate in general. This has been shown LOTS of places other than here, but that you show it yourself and then still say that is… weird.

Judging by other places in the world, a massive and sudden restriction in gun availability might result in some small drop in suicide rates for a very brief period time, but in short order (if not nearly instantly), other methods would be used, instead, and plenty of those methods are both easy and effective (car in a garage, fall from high place, OD on over-the-counter meds).