IndieWeb Search has been intentionally designed to be open. The source code for the project is open. From the early days, there was a basic API that let you retrieve content and featured snippets from search results. I often chat about the search engine and how it is designed. The project is well documented. Another way in which the search engine is open is that all search result pages come with feeds. I hope to see more search engines do this too.
IndieWeb Search was intentionally designed to be open. All search result pages are structured as a microformats h-feed. This means you can use any microformats parser to read a search results page and extract information about each search result. Every search page also comes with jf2, RSS, and JSON Feed versions. You can also parse these programatically to get information about search results. Or you could even subscribe to a search page in a feed reader that supports any of the aforementioned formats.