Problem: Currently Firefox (120.0.1) only displays newly discovered search engines (when visiting a page) inside the extended URL search engine menu, and even in this menu well hidden amoung the previously existing one.
Suggestion: Add notification of newly discovered OpenSearch search engines inside the URL bar, with simple way of adding it to the saved search engines, allowing the user to add an alias etc. ... maybe best, if the settings page is used, to reduce code overhead and double implementation.
BTW, simply adding a search engine via context click on HTML:input fields is terrible as well. Defining a custom search engine (e.g. "https://some.page/q=%s") in Firefox is a mess.