How can the two superpowers cultivate friendly relations / avoid escalating a cold war?

One thing you can personally do is try to cultivate friendships on both sides, and make an effort to share and appreciate the culture, history, and daily challenges of each. If we have populations that really don't want to fight, maybe that will help de-escalate things a bit.

China is my neighbor now (I immigrated to Asia). Some of their literature and history is really quite interesting! I'm not an expert, but I could make a suggestion or two if you like.

What two superpowers?

A recent video by Veritasium tries to answer this exact question : https://youtu.be/mScpHTIi-kM?si=ubCMDqPrrlqYBQI8

I suspect this question assumes that all “superpowers” are the same, namely that they’re all capitalist imperialist states.

They know the answer already, and are probably both trying it.

In US terminology, since that's the language I know, they try for "competition" rather than "conflict". The difference being whether they respect each other's sovereignty for the most part while trying to bury the other, and don't take straight-up military actions.

To achieve this, you provide a long series of "offramps" - opportunities to pause and de-escalate - on the path between peace and MAD, and ensure there is no benefit to either party to do any specific escalation. Mistakes will happen, both deliberate and accidental, but they're very unlikely to all happen at the same time, so even if things get tense there's offramps left, and game-theoretically they will take one because nobody wants a full-scale nuclear conflict.

Superpower wars are expensive and extremely unrewarding. Neither wants them. Sometimes they may talk the talk but when it comes to dedicating the next 10 or 20 years to a constant resource drain with no chance of recovering any of that, they'll find any excuse to get out of it.

What two superpowers?

I'll assume we're talking about the USA and China here.

It may sound reductive, but a peaceful coexistence between liberalism (aka capitalism / other ideologies where private property rights are enshrined) and communism (in this case used as a blanket term for ideologies which are against the concept of private ownership of the means of production) is not stable and will inevitably collapse.

All that needs to happen to avoid a war is for the US capitalist class to keep their grubby greedy hands to themselves. They can't do that though, for capital must grow. They must find more raw materials, more human labour, and more consumers to maintain their profits. They are incapable of cultivating good relations with anyone, let alone anti-capitalist and anti-imperialist entities, because every relationship they enter into is an economic one in which they want to be the exploiters, the winners, extracting obscene wealth from the losers.

The rest of the world is moving in a positive peaceful direction, but I'm concerned about what the capitalist empire will do as it becomes more and more desperate. It's already done some of the most horrific things in human history while in a position of unchallenged or nearly unchallenged hegemony. I can't imagine what it will try when it realizes it's about to lose everything.

Just wait until the US stops being a superpower. It's inevitable.

Only by ceasing to exist.