This has the same problem that most public searxng instances seem to have nowadays, which is that they don't work. Either you just get an error about rate limiting or you get results totally unrelated to your search. I just tried a couple random searches about geographical locations (in English) and got back a bunch of results in Chinese.
I had been using baresearch.org (a searxng instance) but it's recently become unusable, apparently due to the engines it aggregates cracking down on such things. I tried some other instances but they also don't work. It's a bummer because I thought searxng was pretty great for the last year or two.
I've been selfhosting my own to avoid this issue. Once in awhile a search provider will be unavailable but its pretty consistent in pulling in the major ones.
It doesnt require many resource and would be easy enough to run it on docker compose alongside a valkey/redis instance. I have mine on k8s but i dont think there is a helm chart easily found.