Australia hasn't enacted "extreme gun control", nor am I aware of any motivation to reduce suicides. AFAIK, Australia's gun laws were motivated by the Port Arthur mass shooting in 1996
en.wikipedia.org
The UK offers a model on how suicides by gun can be reduced. In the UK handguns are largely banned and those guns that are legally allowed are mostly shotguns and bolt action rifles
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Over the past 20 years the number of gunshot suicides in the UK has declined by over 50% to a little over a hundred deaths per annum. At the same time, firearm legislation has become progressively more restrictive and rates of gun ownership have declined."
This paper reviews the research literature on gunshot suicide in the United Kingdom and the international literature with reference to strategies aimed at preventing gunshot suicides. Trends in gun ownership and changes in firearm legislation in the UK over the past 20 years are described. Most...
pubmed.ncbi.nlm.nih.gov
New Zealand has also see a decline in firearms related suicides:
Following the introduction of legislation restricting ownership and access to firearms, firearm-related suicides significantly decreased, particularly among youth. Overall rates of youth suicide also decreased over this time but it is not possible to determine the extent to which this was...
pubmed.ncbi.nlm.nih.gov
The uk has dropped slightly on suicide since gun reforms, but so have many other nations, australia with just as extreme gun laws only saw a slight drop followed by a surge. Japan which has even more extreme gun laws than the uk has had a very high rate of suicide.
The only odd one out is russia, as their rate was moderate during the soviet union, then went sky high in 1991, then went back to moderate, but despite them having very strict gun laws they also had the collapse of the soviet union and their entire economy well being and way of life.
But the point is gun control has zero effect on suicide rates, people determined to kill themselves are not going to stop because of gun laws when they can hang themselves or throw themselves under a bus or a garbage truck, or jump off a cliff, or electrocute themselves etc. People determined to kill themselves will and no gun control will stop that, and people pushing gun control to prevent suicide are doing such knowing full well it is just disarming law abiding citizens and doing nothing to stop suicide.
Suicide is a result of social factors, stress in peoples lives and most often how much society cares as suicidal people are usually leaving signs and begging for people to show they care before they commit the deed. This means suicide rates have zero to do with firearm access but rather how that society deals with one another. For example japan with a very high rate and strict gun control is a tight knit society but also shuns anyone not in line, which may explain their suicide rate. At a young age they are expected to be high performers in everything and their society shuns what they deem lazy or incompetent.
In japanese society someone who only cleans 500 fish a day may be deemed a waste of oxygen, and looked down upon, and it may lead to that person feeling worthless. In a western society it may be more polite to wonder if that person was ok and if they were cut out for the job rather than shunning them. in Japan suicide has been part of their culture to adress failure going back over a thousand years.
Case and point it is a society thing not a firearm thing on suicide, society has to address this problem itself, and each society does so different which is why suicide rates vary wildly among the world despite firearm regulations.
Edit-- and yes australia did enact extreme gun control, firearms are near banned in australia, to the point being able to own a single muzzle loader requires a bunch of paper work and storage, and their massiove gun buyback was to buyback guns they banned which covered nearly everything but single shot firearms.
thehill.com