The whole war has destabilized the world, more so than the awful Middle Eastern and Afghan wars, because the big powers (at this moment) are China, the US, Russia and increasingly India and Brazil, possibly Pakistan.
Russia's invasion means that the grain which went to feed Africa and elsewhere is no longer flowing the way it should. Hungry people are angry people and it leads to an increase in desperation, instability and conflict - sometimes religious, which has a horrible tendency to spread.
The ecological disaster of the Nova Kakhovka dam will make this worse.
The financial markets have been affected and there is a movement towards the Yuan becoming more of a trading currency, which was previously all in the dollar. The changes are happening relatively fast, though not very fast, but the markets will have to adjust.
The nations that were heavily influenced by Russia are in some cases breaking free, which Russia hates and is dangerous (though it is a good thing for those countries)
There are various other implications but also what has to be noted is that Russia -is- a nuclear power and that can never be forgotten.
Whatever happens now, Russia's stability has been very badly shaken. If Putin stays, he's weakened and he's going to be even nastier - he trusted Prigozhin and this betrayal is going to affect him mentally. He tends to raise the stakes, now lower them, when he's in a corner and this is going to make him even nastier.
If Prigozhin wins, he's a truly nasty individual who built up a truly nasty army and no one knows what he will do to Russia. This is a guy who has people killed by crushing their heads with sledgehammers on film, and then sends a sledgehammer to the heads of the EU. He's a brutal, vicious wild card with no experience of governing, and no one can see what will happen.
If he wins he has no legal legitimacy. I'm not sure how far that's going to matter actually - people will have to deal with him. But it will make things slightly more difficult for him on the world stage.
He will certainly purge his enemies, of whom he has many. He will likely put Russia under a much more severe rule than it is now and it will become more militaristic. When it comes to Prigozhin, I do wonder if the chance of nuclear war becomes more likely - though he's a survivor and it'll be the last option.
China could increase its influence if Prigozhin comes into power, and it might well anyway even if Putin stays in power because he will be weakened. China has a lot to gain from Russia becoming its unspoken satellite - earth-resources but also a potential rival diminished, and a change in power status. Russia used to be more powerful than China, now it's headed the other way very very fast.
So all the stability, which was heavily knocked by Putin invading and the West choosing to stand up to him by supporting Ukraine, was already badly affected specially as food production was heavily impacted.
Now with a vicious psychopath like Prigozhin in charge - the cards have been thrown in the air even further and while people can make some educated guesses which way some of them will fall, no one is sure and there are plenty of cards that we simply don't know which way they will land.