You can activate extensions only “in case of click”, here chrome://extensions/?id=aapbdbdomjkkjkaonfhkkikfgjllcleb
So the extension is only activated when you want. The inconito mode erase the data (cookies, local storage, …) at the end of the session but in my opinion Google use other ways to get a unique ID to identify (anonymously) the browser, when you use its servers.
Also you can use another service, like DeepL wich have a very good quality of translation. But it’s a paid service, there is no free lunch.
By the way I have absolutely no confidence in qwant, the request is forwarded to Microsoft, the worst is that the French government have their nose in it. It’s worse than Google!
I do not understand why it is proposed as a credible Google alternative in Brave …