The Galactic Cold War

Similar to a current potential Cold War with China and the United States, have both sides depend on each other for some degree of resources and economic support. The Soviet Union had a Marxist socialist command economy unlike the United States' market economy, but both nations could theoretically, and for the most part actually, attack each other in covert operations and have one collapse without affecting the economy of another. However, in our modern world, China and the United States both have market capitalist economies connected to the global economic marketplace with both economies being linked. Companies like Disney, the NBA, and American tech companies depend on China for money as well as cheap labor. China owns movie theaters and other businesses in the United States that give the country money and resources. A direct war in almost any capacity could devastate the economy of both nations and the rest of the globe even more than the current pandemic. So, have some businesses for The Colonists trade with specific members of the Outsiders and vice-versa. Show how certain industries would collapse if important Colonist businesses pulled out of Outsider territory and how Outsiders get certain beneficial resources from the Colonists. If one were to attack the other, important resources and commerce would be lost. This could lead to both empires collapsing and others taking their place after economic collapse or damaging effects that might affect one empire more than another, shifting the balance of the Cold War. Basically, have the economies be so intertwined that direct conflict would hurt both sides and indirect economic/scientific/political warfare is preferred.

What you describe is a Mexican standoff:

A Mexican standoff is a confrontation amongst two or more parties in which no strategy exists that allows any party to achieve victory. As a result, all participants need to maintain the strategic tension, which remains unresolved until some outside event makes it possible to resolve it.[...]

The key element that makes such situations Mexican standoffs is the equality of power exercised among the involved parties. The inability of any particular party to advance its position safely is a condition common among all standoffs; in a "Mexican standoff," however, there is an additional disadvantage: no party has a safe way to withdraw from its position, thus making the standoff effectively permanent.

Your Colonists and Outsiders already have achieved the level of MAD (mutually assured destruction) (based on this:'the magnitude of weaponry at each side's disposal means that the first shot of a war could also be the last.'). Neither can advance or safely withdraw. I would not expect further escalation, at least not until the Butchers gather more power. Then they will be able to serve as an external force capable of resolving the existing Mexican standoff.

Proxy wars will be fought. Espionage should flourish. But I seriously doubt that either the Colonists or the Outsiders will risk an open engagement of their troops. If it happens both sides will try to cover it up as fast as possible. The actual Cold War is a very good example of this. Soviet and American troops were frequently present (openly or secretly) in the same war areas but they never officially engaged (or at least there is nothing I know of).

If both the Colonists and the Outsiders can support the stalemate economically, it is quite stable and can last indefinitely.

I would suggest keeping an eye on the Butchers, though. Both empires could and should saw disaccord and disagreement the pirates ranks. The Butchers territory can be used for proxy wars and as a general vent for hawks in both empires. It is also important to prevent the pirates from organising into the third power that can break the existing balance of powers.

"...the magnitude of weaponry at each side's disposal means that the first shot of a war could also be the last."

That's your answer right there. Say that each side has the power to destroy an entire planet all at once (Death Star anyone?) then you've reached the level of cold war that we had in reality. No one wanted to be the first to start a nuclear war because it meant mutually assured destruction. That is the definition of cold war.

Keep the skirmishes small and local, and consider that a cold war is the best climate for a spy story.

If the two sides are two different species and can't live on each other's planets without external life support or thousand years of terraforming, then they might eventually recognise that they are better off if they just start trading the resources they both need.

If they are the same species, then they could seed the surroundings of the gateways with mines that recognise their own ships and blow up when enemy ships come through. Or don't blow up just stick to their hulls and await a command for destruction.

Well, if any gate could link to any other gate, it would be possible to send "cruise missiles" thru gates to destroy the gate infrastructure of the core worlds of the enemy by surprise. The Butchers certainly would be willing to do that even if the civilized people were not.

So we can assume that gates are preset point-to-point connections? It should then be possible to fortify gates connecting to the enemy and equip all gates with self-destruct devices as necessary. This would give the defender a huge advantage in logistics which for two nearly equal empires would result in any attack stalling and rapidly and expensively failing.

We could further assume that leaders of both sides are perfectly aware of this because that is what happened with the last (few) war(s). Attacks failed and ridiculous amounts of resources were expended for no gain other than the reduction of border areas to economic backwaters due to irreplaceable gate infrastructure being destroyed. And of course every gate that is destroyed makes the next attack more difficult.

So there would be a fortified buffer zone between the two empires. Some systems might have lost all their gates and have become semi-independent vassal states. Some of the buffer states might be neutral by treaty. So pursuing a war might be very difficult due to the consequences of previous wars.

That is probably the correct direction even if you want the gates to be less limited or non-destructible. Simplest reason for a war not break out is the previous war. It is also the simplest reason for the war to be inevitable. In general, military always acts based on the last war. So just figure some way for the last war to have been bad enough that nobody sane wants a repeat.

This also means that the end of last war should not have left major grudges or unresolved issues compelling to either side. (You can use such grudges and issues to motivate the Butchers, though.)

Both sides have competent and insightful leaders who wish to maintain the status quo.

1. To the pro-industry party currently governing the Colonists, the Outsiders are useful as they are: an enemy at the gates. A party perceived as pro-military and strong on defense will benefit from an external threat. This party favors industry and rich industrialists and the rich have the most to lose with chaos and war and the most to gain by plowing the resources of the state into military expenditures. Also, nothing unites like a common enemy: fear is encouraged among the working underclass so they will set aside their economic and social issues to support the pro-military party. The pro-military party likes things just as they are as regards the Cold War. Cold War means political stability.

2. The Outsiders are fractured into different factions which cooperate well when there are easy military victories and spoils to keep everyone happy. Despite their top-down organization and militaristic society, the Outsider group currently in power is not confident in their ability to defeat the Colonists. They are fairly certain, however, that even one solid defeat at the hands of the Colonists would lead in short order to a Outsider military coup d'etat. This is bad enough for those in power, but some far-sighted individuals among them fear that an unsuccessful move against the Colonists and subsequent fracture of the Outsider power structure will open the door for the Colonists to move on them in their weakened state and eliminate them as a threat.

Since both empires are extremely dependent upon their gateway networks, any technology which could make gate travel impossible would have devastating effects on both sides.

Each empire has evolve to the point where most of their populated planets are dedicated to a single industrial or agricultural focus. Without the gateways, and the interplanetary commerce which they enable, most of the planets would face starvation and a total collapse of their technological infrastructure should the gateway fail. Billions would die and the survivors would be reduced to pre-technological levels. And the few FTL ships which each empire has kept functional are totally insufficient to make up the difference should the gates go down.

So any weapon, possessed by both sides, which could disrupt or pollute the extra-dimensional space which the gateways connect through, would be a doomsday weapon capable of upholding a tense intergalactic peace.

Expense exceeds potential gains, militaries are rarely mobilized to simply attack another nation there's usually something more at stake like resources a nation wants or doesn't want others to have access to, or a location of strategic importance which again a nation may want or doesn't want others having access to. These empires are being antagonized and may even be skirmishing but with little to gain and no immediate existential threat they can't justify redirecting resources and manufacturing infrastructure to a full scale war effort, put simply to interstellar empires the resources of one system (let alone one planet) are inconsequential