A feature suggest for the function "Search on the current site"

It would be to be able to select our search engine on this function, it would look like this:

It would be to be able to select our search engine on this function, it would look like this:
And if possible, the search engine could be synchronized with our default search engine on the browser
In any case, as far as search engines are concerned, here is a non-exhaustive list of search engines other than google :
-DuckDuckGo (https://duckduckgo.com/)
-Qwant (https://www.qwant.com/)
-Startpage (https://www.startpage.com/)
-Ecosia (https://ecosia.org)
-Llilo (https://lilo.org)
...
Here is my suggestion of the day
Thanks for reading my message