Most browser search engines - even Brave - store your search history to speed up subsequent searches. You can disable it in Settings in most browsers, but then you will have to type in the whole search string every time you want it. You can also periodically delete your search history. Some browsers let you delete it every time you close the browser, also.
It is true, though, that Siri and Alexa are ALWAYS listening, if you are naive enough to have them. Where your spoken words go is anybody's guess.
