I'm an /e/OS user with a Murena account and I had never even heard of Murena being "a search engine". After searching (on DDG), I see that they in June 2025 they launched a collaboration with the Qwant search engine to launch a Murena-branded version: https://murena.com/discover-murena-find-your-new-privacy-fir...

That does not make it "an OS owned by a search engine".