This is a Frame Challenge
People have been "at war" with one another since the dawn of time. It was a powerful image used in the movie 2001: A Space Odyssey. The image of the first ape picking up a bone and hitting another with it. So when you ask "What type of geopolitical status quo can lead to perpetual warfare becoming the norm?" it's a bit silly. Humanity has yet to find a geopolitical status quo that avoids war.
There's a difference between hate and war. You can perpetually hate someone or something. I remember from my childhood a political cartoon by an artist expressing the world's exhaustion (haha, considering it's been 50 more years...) with Middle East tension. The image? Two atoms after the Big Bang, one saying "Hate the Jews!" and the other, "Hate the Arabs!"
So we know it's possible to create a darn-close-to-perpetual hatred simply by looking at the conflict between the Arabs and the Jews, which has ostensibly been going on since the Biblical Abraham divided some land between his progeny — more or less — somewhere around circa 2100 BCE. Yup, four thousand years. If that's not perpetual hatred I don't know what is.
But perpetual war?
Even the distaste between Arabs and Jews hasn't been boiling for four thousand years to that extent. The problem is simple: war requires resources. And resources get depleted.
The (in)famous Hundred Years' War wasn't one-hundred nonstop years of warfare. It had advantages that did keep it going, though. Low technology, slow transportation, slower communication, and long-held grudges (aka hate) allowed it to bubble into war from time to time. But no war can last forever, which is what "perpetual" means. War depends on economic strength, available raw materials, operable manufacturing and training facilities, and above all, a population willing to hate so much that the pain of loss, exhaustion, and desire for peace are completely overcome.
You have problems with all those things.
If you balance your economy so you can fight a war without ruining your economy, it means the war is limited. You can only commit so many soldiers and supporting equipment for so long before you must back away from the conflict. Interplanetary war might, maybe, have a strong enough economy to fight a perpetual war due to having an entire planet to work with — but a believable interplanetary conflict is also limited by the number of ships that can be built and the distances involved. In other words, from a certain point of view, low tech, slow transportation, and slower communication. (Yes, I say "low tech" because once you have fast transportation and fast communication you're tech is too high to sustain a war without all these consequences.) Now, I say this despite the U.S. economy during and after World War II appearing to contradict my statement. But you're missing the point. Axis-controlled Europe was larger than the U.S. and yet crushed economically by the war. The roots that caused those two differences would make a full semester college class, but the fact that the Axis powers couldn't sustain a war for more than a handful of years is really the point here. It takes two to tango.
No matter what you do, you won't have an infinite supply of metal, wood, oil, energy, etc. Materials used to fight a war are, simplistically, lost. They're consumed by the effort. Rationing occurred in every country that participated in World War II. I suspect that a close examination will demonstrate that at least one if not all participants of every war in human history has led to rationing. The truth is, unless you sustain your hate through attrition and continue fighting with sticks, stones, and your bare hands, a war can't be fought perpetually.
The more advanced your technology, the more your nation depends on manufacturing and training to prosecute a war. Manufacturing and training facilities are obvious targets for attack because they reduce the nation's ability to continue fighting. If your nation relies on these to any degree, they're weaknesses that will eventually be exploited. We're back to having so much hate that the war continues with sticks, stones, and bare fists.
Finally, people get tired of war. They tire of losing sons and daughters, friends, even complete strangers. They tire of the increasing burden of keeping the nation running due to depleting human resources (aka, people dying). Good news in the form of victory can keep people temporarily sustained, but a perpetual war will never have enough good news to do this. The inevitable (yes, IMO) end result of a nation's attempt to prosecute a perpetual war is revolution, inevitably leading to the end of the war. To add to this, unless your nation is very small, very homogeneous, and really hates the enemy, there will always be people who prefer peace at any cost over war at any cost. Those people would need to be subdued, even oppressed, leading to increased dissatisfaction among the populace. I don't think it's much of a stretch to say that people hate police states more than they hate political and/or cultural enemies. Could be wrong about that, but I don't think I am.
So, what does "perpetual war" look like?
It looks like the Hundred Years' War: sufficient cultural or ideological hatred to lead to sporadic clashes with time between to allow economies to re-stabilize, resources to be gathered, manufacturing to restore depleted stores, and for the population to relax from war-caused stress.
And that can be had with any geopolitical structure. The U.S. during WWII painted the Japanese people as sub-human. Soviets painted the U.S. as morally weak. Monarchies and tribes have been fighting for eons over everything from land and resources to personal grudges. Even today, all the gloves come off regardless of geopolitical conditions over a good soccer match.
If you believe in creationism, humanity is plagued by the temptations of evil. If you believe in evolution, humanity clawed its way to prominence through eons of competition (aka "war"). Either way, conflict and war is what we do and the proof of our really having become enlightened begins with a desire to stop fighting.
The desire to fight abounds, geopolitics be damned.