I am not the most knowledgeable person on searxng innerworkings so may be wrong, but searxng instances usually use the 'get' and 'post' commands to request+fetch http/https content not an API key. You can get your own api keys/tokens from google and plug them in to searx in the preferences menu if they ever make it API only. There's a lot of IT academic research that relies on google they will most likely never pull API access fullstop but you never you I guess.

There is not much if anything SearXNG instances can do if google changes algorithm. In worst case scenario it can still index other search engines which themselves scrape google like startpage or engines completely independent like duckduckgo, bing, brave, YaCy, ect. Here is a list of all configured engines SearXNG uses by default you can go into preferences at top right of searXNG to configure what engines you want to use among other things.