My take on this is going to be very different even if we accidentally agree on the likely results of increased gun laws.
What grabs the attention of the media (who of course have their own biases and objectives) are the "mass shooting" events that seemingly have any number of conditions and motivations as to why they occurred. No matter if we are talking about the lunatic that went after "sex workers" across Atlanta massage parlors or some other lunatic in a story gunning down random people or dozens of other examples the media will run with the platform of the common denominator it feels it can control. The gun.
At best what is rarely talked about but at worst is monumentally ignored is gun violence occurs every single day in this nation across a plethora of motivations that are ultimately excluded from the debate.
As you point out and some of the sources below confirm is the overwhelming majority of gun violence is suicides, it is not even statistically close how far out front deaths by firearms per year.
What is in second is male vs. male intentional homicides and usually of minority status, i.e. inner city and economically depressed violence. Call it gangs, call it control over drug trade, or whatever else what is not leading the pack are these random acts of violence but rather these weekly if not daily occurrences in larger cities like Detroit, St Louis, Memphis, Baltimore, Cleveland, Chicago, Oakland, etc. The underline causes having less to do with "gun culture" and more to do with sociology and economics.
But that does not move the needle in the world of politics, someone going into an elementary school with an assault rifle does.
As you point out gun control laws will have very little impact on the #1 and #2 motivations and reasons we have gun violence year on year. We have little but some evidence that making it harder to obtain a gun will impact those who want to take their own life. But we have no evidence that people already breaking any number of laws within inner city violence will be less motivated to do so with yet another law.
That is my point, if the demand is there to obtain a gun then US history proves conclusively that the government saying no means criminal enterprise is all to happy to step in and fulfill the demand.
Our issue has always been the same, it was just amplified by gun culture. But the underline reasons are sociology and economics. Those are the reasons why our "homicide rate" is so much higher than comparable nations.
Moreover it means all these political feel good intentions will backfire and in the end the weight of the new laws will end up falling squarely on the backs of minorities in these already depressed areas leading to even more unequal application of the law and even more minorities in some phase of the criminal justice system. It is taking the 'war on drugs' mentality and doubling down on the effort. Who ended up most impacted? Minorities, and we have no evidence things will be different this time.
Mass shootings are going to happen, but that is not our real issue. Those instances are just splashy headlines grabbing for political reasons via a largely complicit media.
Deal with actual people (again, sociology and economics) and we might get somewhere with the real reasons we have so much gun violence.
It is worth noting that politically speaking the CDC is limited in how far they go down the analytics route on this subject, and some of the available stats with analysis are a few years old.
Various sources for one to consider:
The data in this interactive graphic comes primarily from the Centers for Disease Control and Prevention’s Multiple Cause of Death database, which is derived from death certificates from all 50 states and the District of Columbia and is widely considered the most comprehensive estimate of...
fivethirtyeight.com
Review some basics on firearm injury and death, including a description of deaths from firearms by type and the economic costs.
health.ucdavis.edu
Gun violence in America is at a crisis point. Every day, 125 people are killed from guns and more than twice as many are shot and wounded.
everytownresearch.org
While the number of gun deaths in the U.S. fell for the second consecutive year in 2023, it remained among the highest annual totals on record.
www.pewresearch.org