Your best bet is to find a car where its easiest to disable the antenna/cellular modem for, so look for a car that has a fuse for the DCM(digital communications module) you can pull, as having it be a fuse means you can readily reconnect it should you need to, try to find its schematic online, or find the repair manual for the car or use a car maintenance program,
Apparently its also possible to call the car company and ask for an opt out when serviced,
I vaguely remember some people experimenting with replacing the head unit with aftermarket ones, but no idea how well that would actually go in practice
This is probably the best resource for keeping track of which search engine options exist and what their quality is like: https://seirdy.one/posts/2021/03/10/search-engines-with-own-indexes
For a “fire and forget” option that doesnt require any configuration you cant go wrong with good ol DuckDuckGo: https://duckduckgo.com
If you’re okay with dealing with more configuration and breakage then Searx can be pretty powerful as its a metasearch engine that can search with every search engine you tell it at once and agregate the results(while proxying things to maintain privacy): https://searx.space (had decent luck with the https://search.sapti.me instance if you just wanna try it out without searching through a list of options)
Also all search engines are kinda bad due to SEO spam and “AI” generated images and articles polluting the results, consider using uBlacklist to help you filter out the trash from search results(think of it like ublock origin for search engine results), can use it for basically any search engine so no reason to not set it up: https://github.com/iorate/ublacklist