The API on demo.pygeoapi.io has been indexed by Google Search too. Because the HTML representations are fully kined (from the landing page, to collections, to items and browsing through them), Google could index the data too.
See for example: https://www.google.com/search?q=site:demo.pygeoapi.io
And browse through the pages. After a few pages, individual items are found: https://www.google.com/search?q=site:demo.pygeoapi.io&start=70