The original creator/BDFL (Dylan Araps) has been a bit off and on with activity over the last year or so, so the official repository is a bit out of date. The community has kept up to date main and community repos at https://github.com/kiss-community/ though. Come chat with us at #kisslinux on libera.chat!
Also as pointed out in other comments, the main URL is https://kisslinux.org now. Dylan never could seem to settle on a domain name for whatever reason, so there are many dead links, and I don't blame the OP for not finding the most recent one.
Searx is not a search engine with its own index, but rather, it is a meta-search engine, and operates by forwarding your query to a customizable list of other search engines (like Google, DDG, Wikipedia, etc) and gives you aggregated results. It is more privacy respecting, because the search providers cant run any tracking JS, see your IP, give you tracking links, etc. People may have their own instance for any number of reasons, including: hosting in different places to get different geo-specific results, to be faster by being closer to the end user, to change default themes/settings, to reduce the load on other instances. Nowadays, the fork SearXNG is more popular than the original.
Also as pointed out in other comments, the main URL is https://kisslinux.org now. Dylan never could seem to settle on a domain name for whatever reason, so there are many dead links, and I don't blame the OP for not finding the most recent one.