(not OP but same boat) Doesn’t really matter to me because google knows my servers external IP which is a non-issue: I don’t expect google to try to attack me individually but crawl data about me. There is no automatic link between my server and my personal browsing habits.
In terms of attack vector vs ease of use , self hosting searxng is a nobrainer for me - but I do have an external server available for things like that anyway so no additional overhead needed.