I think we'll implement the basic functions of capitalism in software, and learn to use them on a smaller and smaller scale, to the point where you could issue a bond to buy a burrito and sell your burrito farts, someone else could buy the bond, the burrito gets eaten, and dividends paid in the span of an hour.
As that technology diffuses, large corporations will lose their competitive advantage over individuals, and we'll switch over to voluntary contracts for all commerce, instead of coercive employment and property regimes. There will rarely be a time when you think "well, this deal isn't great but I don't have a lot of other choices". You'll be able to just decompose the deal and bid out its parts to an effectively infinite network of contractors, and bond it out in tiny increments. Any business plan which makes sense will be immediately implementable.
Simultaneous with this, we will also develop softwares for other political organizations besides capitalism, including communism, monarchism, fascism, etc, which we will all participate in voluntarily in the same way. Anarcho-syndicalism will be notable among these, because it is the only one with a mechanical basis in consent and a morality grounded in self-defense.
In this new regime, where people are no longer dependent on large cultural institutions for basic sustenance, consent will become a much more valuable marketing tool. People won't be used to being pushed around, so pull-based institutions will start to work better. Anarcho-syndicalism will have a powerful advantage in this market, and people will shift over to using it for most of their daily transactions. These will have to be mirrored with capital-based accounting in order to be legal in capitalist states, but the actual people involved will think less and less in terms of capital. You will come to my bakery and ask for some bread, and depending on the rules of the syndicate, I'll give it to you. In the background AIs will note a "sale", a bond if necessary, and file tax forms, but you and I won't look at them. Anarcho-syndicalism will be how we make decisions, capitalism will just be an accounting method required to not be put in jail for illegal distribution of bread.
Eventually the capital accounting will be ignored for most things, certainly basic healthcare concerns like housing, food, mental health, maintenance of sacred lands, etc. The capital contracts will still be used in the entertainment industry, which will make up the vast majority of GDP. And even within that industry, corporations will be a minority. Most work will happen inside small partnerships of 2-10 people who are working directly together, said partnerships also contracting out to the individuals as sole proprietors. Full time employment will be extremely rare.
The economics of this are based on the presumption that human health is inherently valuable, so bonding it is no problem.
In this way capitalism will "die", still existing but no longer being a central conduit of resources and power.