https://ottawa.ctvnews.ca/cheo-joins-other-children-s-hospit...
While that's not the same as saying actual deaths from suicide have increased, there is a serious problem, at least here in Canada.
edit: Attempts up 90% in Colorado as well:
https://coloradosun.com/2021/05/25/mental-health-emergency-c...
Suicide is a serious issue and shouldn’t be ignored. We should also apply the same logic to suicides as people are applying to covid - would these people have tried suicide anyway but covid/lockdown just brought it forward? Will we therefore have a drop in attempts now to mirror the spike up?
While a children's hospital in Colorado might have reported a 90% increase, across the whole of the US suicides were down 5%.
As far as I know, most countries are reporting an overall drop in suicides during the pandemic.
For your other point about excess mortality being caused by lockdowns, you can view charts of excess mortality here: https://www.euromomo.eu/graphs-and-maps/
You can see that some countries, e.g. Norway had lockdowns but did not incur any severe excess mortality - but note that this only proves that you can have lockdowns with no excess, not that every lockdown is equal.