I’ve been using a Safari extension called xSearch to change my default search engine and also used to change Reddit.com to old.reddit. xSearch for Safari on the App Store
Since iOS 17 the app changed permission requirements and now it must have full access to browsing history.
Although the developer states that no data is collected from the extention and that the permission is only used for the current website, I still stopped using the app.
I really liked using this extension and there are also no other alternatives.
It also needs access to your Safari default search engine website, so you still need to trust them, but the App Transparency Report shows the app doesn’t connect to any domains iirc.