Google still lets you do some things without logging in but that doesn’t mean that they don’t build profiles or try to link them with other activity sources. Most of their revenue comes from advertisers paying for targeting.
I am not paid to design kagi architecture nor I know the internals, but let’s say I can host that mentioned anonymizer myself (say in Canary Islands), and it pulls the queries from kagi who you have paid for by monero, then the company knows nothing about the user, no profiling, no tracking, nothing, that’s a great starting point.
If this doesn’t exist, using something like searxng is far better (privacy wise), not just as mentioned on how it’s more anonymous, but also it gives you the ability to blend in, rather than looking like a sore thumb in the logs.