Interesting thoughts. I've always liked if we could have something like an `api.txt` file on a website, just like we have a `sitemap` file.
The `api.txt` can simply be a text-based listing of links to API descriptions for all APIs exposed by that site publicly. Most API description formats already allow for the API name, category, endpoints, etc. so no need to reinvent the wheel there. A good idea would be to add the `<link rel="api" href="api.txt" />` tag on the webpage too. This would make discovery and cataloging much easier.
Some API cataloging sites have come up with interesting ideas. For example, there is a service https://sdks.io/ that can automatically generate SDKs right out of the API descriptions that they have crawled. It is powered by https://apimatic.io/