Want different search engine than offered in ios.17.5

That's all we can do for now.

You never need to use Chrome. No one does. Brave is Chrome without the Google.

Brave also has its own search engine, but if you prefer Google's biased, censored, limited search results you can always use Startpage. It performs a Google search, but removes all personal tracking information prior to sending the search query to Google.

That is not an option

If none of the options appeal to you, then simply designate the search engine you want to use as a home page. There are plenty of alternatives other than the ones Apple incorporates as choices.

There is simply no justification to use Chrome, ever, on any device.

You can select google, yahoo, bing, duck duck go, or ecosia as your search engine in safari settings