Great point. The SearX documentation addresses your concern here [1] I run my own, for myself only (via WireGuard). Its easy to set one up, for example with Docker [2]. However, I recommend to try it out first. A list of public instances is available here [3]. These lists include Tor entries (if you require anonimity, don't enable JS and use e.g. Tor Browser!), and also mention where they are hosted (if on clearweb). You can try it out there. That being said, one which seems safe (because of the people behind it) is [4]. At least safe to test it.
Wouldn't running a private instance be the same as directly queryint google? Like, it queries through the same IP you use, and can build a profile just using that.
[1] https://asciimoo.github.io/searx/user/own-instance.html
[2] https://github.com/searx/searx-docker
[3] https://searx.space/
[4] https://search.privacytools.io/