In general the biggest breakthrough in that space has been machine learning powered relevance scoring and NLP. PageRank worked by using high level metadata (links between pages). We now have methods that can incorporate metadata information and analysis of the content itself.

Sure, SEO gammification(TM).

You didn't specificy that the breakthrough needed to be useful to the users or the people wanting to monetize search.

yes https://youtu.be/6HYdTtIoyts

This is a video about the "21e8 index". I have never heard about that. There seem to be one scientific paper about it, by Provides Ng, "21E8: Coupling Generative Adversarial Neural Networks (GANS) with Blockchain Applications in Building Information Modelling (BIM) Systems" from 2021 which does not have any other citation. Also Google does not really provide any information on 21e8.

How is this a representative example?

Proof of work to rank pages? That sounds like the worst idea I’ve ever heard. I’m no fan of Google injecting ads into the top spots of their results but at least you can get to the “real” results by just scrolling down. With this paradigm, every link becomes paid “ad”, and the ranking is completely dominated by companies and individuals with big pockets, not any objective or even subjective measure of the quality. And they’re all ads paid for by wasting energy.