There's no reason to believe that cancers missed in the past 8 months would have appreciably immediate consequences as there's not much that can be done about late stage cancers. Plus, like suicide, cancer deaths are obvious and I haven't seen any substantial increase in those numbers.
Finally, studies from just a couple of months ago studying cardiovascular disease deaths showed that there's been a decrease in those deaths. It's hypothesized that deaths from early intervention (e.g. bypass surgery) have been avoided, and the expected increase from untreated disease is still further out. Even if deaths from untreated CVD are finally upon us (post study period), it wouldn't substantially effect mortality numbers from the previous 8-month period.
In other words, it's easy to subtract these things from all-cause mortality. But AFAIK doing so doesn't significantly change the numbers.
Furthermore, there's little reason to doubt the potential lethality of COVID-19, given the hard and indisputable CFRs and IFRs from Italy, New York, and Wuhan, all of which occurred during a very short period of time, and largely before significant mitigations were put into place. Thus, while mortality rates clearly vary across different regions, there's little reason to believe that this fact alone disputes the inherent lethality of COVID-19, but rather reflects environmental (including social) differences across regions and across time, and thus little reason to believe that mortality increases elsewhere are principally the result of anything but COVID-19.
The sun may never come up tomorrow. Aliens might land and wipe us out in the next hour. You might spontaneously quantum teleport to Alpha Centauri while reading this reply. These are all possibilities. But possibilities aren't probabilities; they're two different things. Merely suggesting that something is possible does not refute the probable likelihood of an alternative. Conflation of those is what makes FUD (Fear, Uncertainty, and Doubt) seem credible to the naive or wanton contrarians.
The evidence for that is quite weak.
Overall, the literature on the effect of covid-19 on suicide should be interpreted with caution. Most of the available publications are preprints, letters (neither is peer reviewed), or commentaries using news reports of deaths by suicide as the data source.
In general, it takes longer than nine months to go from cancer screening to death.
We don't actually know that suicides are up, because the data is yearly (which is a problem we should probably solve).
All cause mortality is a rough number, but it's the only one that will eventually allow us to measure the impact of the pandemic in a few years.