You ask a very interesting question, that to me speaks to the future of education gets to the bottom of education entirely.
Right now, education focuses on getting people through the system so they can attain a credential. It teaches us, primarily, how to get one over on the system, how to look for loopholes and shortcuts. It creates a culture of corruption, of looking for approval from institutions in order to move up in life.
What does a world where anyone can learn anything they like for free very easily look like? Well undoubtedly it looks like a place where a lot of people don't learn much, because they have no interest in learning. But it also looks like a place where people who are interested in learning can and do learn endlessly if they like, the opportunity for anyone to get educated to a degree reserved for elites that most of us could only dream of even two decades ago is upon us. Writing the paper won't be about proving you wrote the paper to some authority figure, because it's no longer proof that you wrote it. Writing the paper will become about helping yourself understand something you want to understand.
So to your question, what is the future of proving that I know something, the future is you can't prove you know something, there's nobody to prove it to and you know things because you want to know things, because you recognize the value on knowing them beyond "this piece of paper qualifies me for a job." The future is the truth that we have been pretending isn't true for a century: that no matter what you try to do, those that want to learn will learn and those that don't won't, and their lives will be what they are on their own merit and of their own volition.
If you want to call yourself educated, the only person you need to be proving that to is yourself. We have entered a world of information post scarcity, which necessarily comes with post scarcity of noise, distraction and disinformation. The competition to understand things and the benefit that comes with understanding things will get stiffer, but access to that competition will become egalitarian. There will be a great divide among people: those that follow the noise of the day and those that continue to learn freely of their own volition.