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.
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.
And US drug overdose went from 72k in 2019 to 81k in 2020. So less than 2% of the economist's 500k[1] might be attributable to that.
You might point at road deaths, which have increased quite strangely, but again, wrong order of magnitude, by 2 orders even, increase of 4k compared to 500k.
So to answer your question, no, it's not a questionable assumption.
Perhaps you might consider the simplest explanation, a deadly virus, is the best one?
[1] https://www.economist.com/graphic-detail/2021/04/05/deaths-i...