Unfortunately the deal between Mozilla and Google only allows Google to be their search engine, rest, they are told to bring only Bing and search engines that indexes from Bing. StartPage, Mojeek, Kagi, Brave Search, well, it isn't. I have tried adding them and hoped and checked they would synced with my Mozilla Firefox account, but when on installing of another instance of Firefox, none were found and Google was back to my default search engine.