There just aren't competing colonial or imperial powers anymore. WWII and the agreements between the western powers directly afterwards set the stage for one imperialist power and many vassals. While non-US western countries certainly have their neocolonies and partipate in empire, they have no means with which to stand on their own as imperialist powers.

I think we are already starting to see what a multipolar world looks like: cross border cooperation to improve everyone's material conditions.

Maybe, maybe not.

There's only one imperialist bloc that towers over all the others and sucks all the oxygen out of the air and that's the US led order compromising all of NATO, the EU, Australia, New Zealand, and hanger-on occupied Asian vassals like Japan, occupied Korea.

The most Russia can do for instance is align with anti-imperialist blocs like BRICS for protection and do some minor supporting of anti-US actors by proxy in Africa and elsewhere. Ukraine is going alright for Russia but it's a definite drain, they didn't want it to start with and made it worse with years of avoiding it, they still don't want it and they don't want another fight though the US is intent on trying to start more skirmishes between them and say Georgia and Moldova but neither present the kind of military that Ukraine fields and would last very long even if Russia had the appetite to confront their neo-liberal aggression against it and Russian people.

I could see say India or Brazil doing some regional imperialism but not against other potential imperialist powers like each other or Russia. These might at times butt up a little against US interests but I don't think it will escalate to open war because no one wants to fight the US. Maybe once the US has their Suez Canal moment and they look like a paper tiger more chances will be taken but even then I think that has to happen plus the end of US dollar hegemony as well otherwise they just ruin you or inflict great pain greater than the gains you could get through those financial means and sanctions. Mostly we see angling and hedging of bets. Various countries trying to do things for their own interests against US interests and with the interests of other powers or power blocs but avoiding pushing it so far that anyone wants to go to war over it. You see Turkey doing this kind of angling and there are countries like Hungary in Europe who try and maximize their own benefit by not being drawn too closely to the side of any one power and playing the various powers against each other while avoiding directly angering any of them to the point of confrontation.

You might be interested in....

Levy, Jack S. (June 1998). "The Causes of War and the Conditions of Peace". Annual Review of Political Science. 1: 139–65. doi:10.1146/annurev.polisci.1.1.139

...even if you don't read a lot of academic papers.

There's 'hegemonic stability theory' and 'balance of power theory'. The first says unipolar is more peaceful (think Pax Romana, Pax Mongolica, Pax Americana), and the second says multipolar is more peaceful.

Levy says that two regional powers of similar strength are less likely to go to war when the globe is dominated by a single power.

"The dyadic-level “power preponderance” hypothesis, which holds that war is least likely when one state has a preponderance of power over another and is most likely when there is an equality of power, has received widespread support in the empirical literature (Kugler & Lemke 1996)."

Bremer SA. 1992. Dangerous dyads: conditions affecting the likelihood of interstate war, 1816–1965. J. Confl. Resolut. 36:309–41, https://sci-hub.se/10.2307/174478 supports balance-of-power theory: "After reviewing the empirical literature on dyadic power and war, Sullivan concludes that "though the findings do not speak with one voice, a tendency seems to be, with some certain exceptions, that situations of preponderance are more likely associated with nonwar than the opposite"(1990, 129), an assessment with which I essentially agree" (See also the 0.36 number for large power differences in the paper's results table). Though note that that study looks at pairs of countries, not at geopolitcal superpower structures. This contradicts the Levy paper which says "there is substantial evidence that at the dyadic level an equality of capabilities is significantly more likely to lead to war than is than is a preponderance of power (Kugler & Lemke 1996)"

TL;DR academics disagree on whether unipolar or balance-of-power leads to more war