What do you think will happen when the capitalist economy reaches its peak and it is not possible for it to grow more?

This is what neoliberalism is. Capitalism did "peak" in the 70s or so for the imperial core, when it created a crisis it couldn't actuslly resolve. Since then it has been cannibalization of industry and the welfare state domestically, the same for unfortunate countries subjected to the IMF (i.e. US imperialist finance), and financialization bullshit that makes numbers go up but is actually a drag on production and makes things even less stable.

Outside the imperial core, there are still experiments being done. Depending on whether you want to apply the term capitalism, China's approach to markets clearly hasn't peaked. I'm not even sure what will happen there as they massively improve quality of life and productive capacity while facing relentless attack from the imperialists. You could imagine crisis and you could imagine steering around it (with cost) as they did their real estate bubble, perhaps socializing further in response. Basically, I'd like to imagine that China develops and maintains the capacity to break down, piece by piece, capitalist relations within its own country as a way of responding to crises of capitalism. But you could also imagine an equilibrium where capitalists retain too much influence and ahit gets fucky.

Look around you

I see a couple of dogs, some walls and a tv
- oh thats just being silly

Every seen a snake try to eat itself?

Global capitalism loves to eat the lowest hanging fruit first. Think of the global south countries exploited in a multitude of ways. As multipolarity increases, the fruit become more difficult to reach. So the exploitation moves to the next easiest target.

Currently that means the mid tier countries that are also invested in the global capitalist order. These are like the lower and middle managers. They are trying to climb the ladder to be like the big bosses, but that just makes them easy marks for exploitation because they believe the marketing.

Eventually the layers of the easily exploited gets peeled back until the exploitation so common elsewhere starts to come home. This has been happening in various forms for the last few decades, but it will continue to intensify.

This is just a long description of what is known as colonialism turning inward.

To reach it's theoretical maximum, Capital will have to burn all human beings and all of the rest of nature as fuel. Otherwise it is missed growth for which shareholders may hold the board of directors liable.

A war with China is how innovative disruptors will move fast and break things all the way to the moon. We're going to be tired of winning, folks.

Peak capitalism is when robots with LLMs slightly better than current roam the charred remains of earth talking to each other in nonsense language because they're constantly training on each others speech patterns and every little error adds to the snowball of nonsense. This is progress.
To reach it's theoretical maximum, Capital will have to burn all human beings and all of the rest of nature as fuel. Otherwise it is missed growth for which shareholders may hold the board of directors liable.
i just love being a cell in the entropy beast

Fascism

War. That one's easy.

It doesn't need to be universally trending up, it just needs to be locally trending up. Destroying a bunch of stored value is a really good way to get the humans subjugated into building the stored value back up again.

I think at this point ICBMs and MAD put a damper on war as an option to really burn dead capital like they could in WW1 and WW2. They don't even like foreclosure and failure as an option for zombie capital, it's all state supported. It should be imperialism and inter-imperial wars but we might need some newer analysis in this really deeply warped state of capitalism.