The regular way is to visit the homepage for the search engine you want to add and click the URL bar. This will show the usual search drop-down with the "This time, search with:" row at the bottom. If you're on the homepage for a search engine which hasn't been added to Firefox, there will be an additional button on that row allowing you to add the site as a search engine, which will make it accessible from the regular settings page like every other search engine.
That said, keyword searches are awesome and I use them for a whole lot of things, including effectively custom search engines. I have keyword searches against, e.g., internal confluence docs so I only have to enter "con <thing I'm searching for>" and firefox will load the confluence search page, or "people <name>" to bring up our internal phonebook with a search for the employee. I don't think I've ever needed to add my own entirely custom search engine to the browser.
(My impression is that the feature is hidden behind a setting because it's half-baked and not yet ready to replace opensearchdescription xml, add-ons, and bookmark keywords as the official way to add search engines.)
For those with tech knowledge who want to try to change things, I recommend checking out https://www.techcongress.io/, https://horizonpublicservice.org/ (they both have a cohort they're recruiting for right now) and USDS.