if you looking for a good alternative for google search, try "SearXNG"
actually awesome and fast search engine (depending on which instance you use) with no trashy AI and ADs results also great for privacy, if you don't know which instance to use go to https://searx.space/ and choose an instance closest to you
If you are on a desktop, you can run it locally, you are much less likely to be rate limited, but this comes at cost of your ip being still visible to google or whatever search engine you choose to scrape from
IP addresses are not some super-secret PII. You don't have to try to hide it unless you don't want to reveal the country you're in. You can also proxy SearXNG through tor. Though Google wouldn't work then, and of course search time increases as well.
Your IP is waay down the list on the fingerprint vector. Go to fingerprint.com, connect to a VPN, hard refresh the page. They'll know you're the same person. Nobody uses IP to fingerprint people. SearXNG mitigates a lot of the things that they actually use.
I completely agree with you, and what i wrote was in haste, essentially, what i wanted to say, was that an individual running searxng does not provide the anonymity benefits you would get by using some public instance, but it it still better because you are not directly using google or whatever website, and now searxng kinda acts like a browser between you and them, which does limited conversation - there aren't any js based fingerprinting. I also use searxng locally, i cant stand the constant rate limiting of public servers, or sometimes only a few engines are blocked, and variation in result quality is unacceptable to me. I just wanted to add that bit for transparency,