A trick I’ve learned for when this happens with SearXNG is to add “!web” to the search query. It provides a wider range of search engines and images, which specific ones can be selected in the settings. Like all things software, it takes a bit to adjust to a new interface but SearXNG allows users to control a lot more of the functionality.
I don’t have an extention on FF but whenever I copy a link there’s an option to also copy clean link. I’m not home, but I believe this is associated with my search engine being SearXNG.