What Causes Warfare?
It seems that warfare generally is triggered by one or more of three primary causes.
1. Religious conflict
This is your catch-all for various forms of holy war. Whether this is Mayan civilization going to war to capture sacrifices to the gods or religion A saying that religion B is the evil and must be removed from the planet, it fits here.
This category simply won't apply in your fictional world. All the religions agree: mass violence is going to get you all killed, so don't do it. Even when they worship someone else, this rule still applies.
Centuries of gods saying "NO!" means that you're unlikely to garner much support for religious violence.
2. Cults of Personality
Strong leaders often secure their power base through warfare and violence. Despotic Third World leaders, ancient Bronze Age kings, and even gang lords all fall here. Find someone, label them the enemy, and then rally your troops to your side. As long as you can convince people to attack those people over there, they won't look too closely at what you're doing over here.
Again, your religion will provide a strong deterrent to this sort of warfare. "Go destroy the kingdom of Oz, for they are the enemy!" is much harder to pull off if lightning comes down from the heavens (or a priest comes in with poison...) and kills you for trying to drum up a war.
Centuries of gods saying "NO!" means megalomaniac rulers are probably going to be unpopular.
If your people have no food, no natural resources, no water, and/or no hope, it becomes far easier to build up support for warfare and civil war. Throughout modern history, many wars have sparked because there simply wasn't enough stuff to go around -- food, money, whatever. This could be because your area is short on raw materials or because of economic depressions or drought or any number of subcategories.
The world you describe hasn't solved the suffering that's behind this root cause...
What does this mean for your people?
With 2 of the 3 primary causes more or less removed from play, it seems that the root cause of warfare will most often come out of economic concerns.
So what does that mean? You won't find a king rallying support for war as a way to distract folks from their woes or to focus their anger on an external target. But the anger will still be there, unfocused, waiting to flash up.
So your savvy rulers will be aware of that, and that they can't overtly focus the anger elsewhere. But they could build up support for the sort of non-war violence we see all too often.
State-sponsored terror isn't war. but it's sure a tool used to focus anger elsewhere.
Trade wars aren't really war. But they still are a way to focus anger and keep control of a people by "attacking" some other group.
Public relations wars are another, often used alongside trade wars. This was common enough during the Cold War: USA or USSR would make brash statements about what terrible things the other nation was doing somewhere or other, all the while doing things just as bad on their own... (Disinformation, psy-ops, propaganda, would all be tools in this box.)
Competitive Events / Sports Look at the Olympics and how intense the rivalry between USA and USSR was throughout the Cold War. Team and individual sports could easily become a mock warfare stand-in. Or perhaps "duels" where the challenged picks the format. Imagine if a country wanted to "fight another, and they chose to fight by bake-off, Mario Kart race, or spelling bee. With the equivalent of Switzerland or the UN working to quantify the rules and then sending judges to oversee the events. And, yes, pistol duels would quite possibly exist here, too.
Technology / Innovation USA never would have landed on the moon if we hadn't wanted to prove we weren't, somehow, superior to USSR. The entire space race between the two nations was a proxy war of a sort. Races to specific, quantifiable, goals would be a challenge for superiority.
Assassination would still exist as a means to settle scores. Oh, it might require more subtlety than snipers or whatever, but there would still be folks who would try to solve their differences by 1-on-1 murder.
Germ Warfare might become a tool. Spreading a plague isn't mass combat, so it might happen. Though it would be no less morally acceptable, there's no reason to believe it wouldn't be used.
Threat of actual warfare might exist? This is a bit sketchy. After enough generations under the gods' rules, the very idea of mass combat would be lost from common thoughts, so it seems unlikely that anyone would consider the threat of actual warfare and meaningful deterrent, but it might? If you tell folks you're willing to risk the gods' wrath to get what you want, they might not be willing to risk it. I suspect this would be roughly on par with threats of nuclear war -- a threat, but one so terrifying that no one really wants it to happen. Or at least, no one who's sane, anyway.
Cyber war would certainly be a thing, once technology reached that level. Hacking your enemy doesn't kill anyone, so it'd be a primary attack front.
Bluff Note that from each of the above categories, you'd have not just the actions themselves, but the threat of these actions as meaningful tools to get what you want. Just as the threat of actual warfare (diplomacy via aircraft carrier) is a thing in the real world.