As to the question of "who should have standing to initiate a proceeding?"
I would answer, "anybody who is willing to suffer the consequences and pay the costs associated with initiating a bad faith proceeding or abusing legal process."
In short, a red flag gun law statute should have a provision that any individual who is found to have initiated a proceeding in bad faith or for an ulterior purpose, shall be liable to pay statutory damages of $25,000.00 dollars to the respondent in the proceeding as well as all attorney fees incurred by the respondent and the court costs associated with the proceedings that were initiated. A conclusion of bad faith shall not rest solely upon the respondent defeating the petition, but must require a showing that the petitioner lacked any reasonable basis to believe that the respondent was a danger to himself or others, or that no reasonable individual would have concluded the respondent was a threat to himself or others, or a combination of such factors."
An ex-girlfriend initiating a proceeding to compromise the firearms rights of her gunsmith ex-bf, while she knows he is not a threat to himself or others, would be a classic example of bad faith and an ulterior motive.
That would likely provide sufficient basis to prevent a neighborhood Karen from initiating a proceeding on the basis that she doesn't like her Marine vet neighbor who flies the Don't Tread on Me flag alongside the USMC flag while sporting a MAGA bumper stick on his truck, but people would likely feel empowered and safe enough to initiate a proceeding to head-off the next Bath School disaster.
A rather interesting question, particularly in light of the fact that my main term paper in law school was on the exact topic of mental illness and the implications for firearms rights that a mental illness diagnosis has, and covered firearms rights for the mentally ill, formerly mentally ill, different standards of review used, and this was back when only one or two states had "red flag gun laws." It is about 4,000 words and I would be glad to share it, but unless you have an intellectual appreciation for the law and legal analysis, a law degree, or a particular interest in a discussion on mental health and firearms rights/laws, it will probably be dry and boring. Some of the focus is on the [then existing] circuit split with the 6th Circuit using intermediate scrutiny and the 4th circuit using strict scrutiny. However, as my paper was pre-Bruen, and we now live in a Bruen world, a lot of the legal arguments/analysis in my paper are sort of obsolete or focused on standards of review that are likely no longer current.
My conclusion was that nothing much will happen in regards to progress due to lack of interest in pursuing serious solutions, lack of understanding by judges of mental illness (almost all judges lack medical/psychological backgrounds), lack of safeguards for individual rights, and ultimately deadlock and gridlock preventing any workable or viable solutions.
The approach of, "let's pretend mental health is great in the USA and continue doing nothing other than drugging teenagers and young adults with Big Pharma dope and then wondering how and why they are melting down and gunning down people in public" obviously hasn't been working.
I suspect the Second Amendment in the USA is going to die the death of a thousand cuts because of the refusal of society to do anything about the dangerously violent mentally ill people in our midst, while burying our heads in the sand and insisting, "I don't want any law passed that might be useful for curtailing the mentally ill from going postal, because in some scenario I can conceive of, it could or would be used against me or abused against me." Eventually, the average American is going to throw their hands up and shout, "enough is enough, I'll accept any offered solution" and some slick smooth talking politician is going to come along and pitch them on a total gun ban or a total semi-auto ban. We're at a point where the Second Amendment can plausibly go either way of "total restoration of all major rights, end of most federal regulations" or "a near complete civilian ownership ban." Either one could happen in the next 5 years.
Approximately 20% of American adults have an active mental health diagnosis, post-Plandemic it is probably hovering closer to 30-35% of Americans. Hell, about 35% of middle-aged women are on SSRIs. If the best we can come up with is, "under no circumstances can any guns ever be taken from anybody for any purpose no matter how compelling the justification or the reason, because, muh rights won't be infringed" then we're going to have a whole hell of a lot of Charles Whitmans climbing towers and it is ultimately only going to be a matter of time before the bulk of people, looking for a one-size fits all, easy fix, "no brainer" solution, decide, "well let's just ban all semi-automatic guns and be done with this."
The NFA was closed to post-86 machine guns for civilians in 1986. If a lawful NFA holder snapped and used an M2 Browning to kill 500+ people at some public event, that might be all it takes to spur a nationwide NFA round-up/confiscation. If NFA guy began to hear voices, telling him he was the angel of death and his mission is to "usher in the end for the wicked" and he was telling his friends that he has a "sacred mission" and the details of this supposed mission, somebody should be able to utilize a legal mechanism to intervene before there is a triple digit body count.
82% of Americans are vaccinated, and I have never found any stories of any Americans using force to oppose police/Guardsmen who were doing door-to-door gun confiscation in the New Orleans area in the aftermath of Hurricane Katrina. As a practical matter, if there is a nationwide gun ban in the USA, particularly if it is "only" applicable to semi-autos, I predict the vast majority of Americans who are covered by the ban, will at best peacefully disobey, many will affirmatively comply, virtually none will engage in violence over such a thing.
A friend of mine once described the situation as, "hopeless but not serious" meaning the situation is dire and nobody takes it seriously.
There is a blatantly colossal problem with mental health in the USA, we are effectively offering no solutions, so we shouldn't be shocked that those who despise are stepping up to fill the void. Approximately 60,000,000 Americans as of 2021 had an active mental illness diagnosis, with the most common being depression and anxiety, followed by bipolar disorder. If these problems are going to be addressed it would be nice if they are addressed by people who are not ideologically against us and who are publicly committed to mass disarmament.