Click the URL bar. If on a page that provides a search engine, you can add it immediately. If not, click the cog on the right, then choose a new default search engine.

Kagi has an extension that just switches it for you in Firefox

Really? Open Settings, there's a "Search" tab on the sidebar. Literally the first item is "default search engine".

At the bottom of that tab is the "Search shortcuts", which makes it trivially easy to have multiple search engines installed and use the one you want from your search bar. (I use @g for google, @d for DDG, and @k for Kagi, with an @v for DevDocs.io)

Firefox settings has a search bar, but don’t worry, it doesn’t use Google as it runs locally. /s