I guess it's time to stop searching from the url bar (sorry, "awesomebar") and create a local html file as the startup and new tab page, with search boxes for all your fav engines. Just like the good old days.
I was able to set a local file for new windows, but it looks like there's no built-in way to set a custom URL for new pages, not even in about:config (v125.0.3, Fedora). :/
I may have to simply use the URL bar with data collection opted-out, as I'd rather not bother with vetting and installing a custom open source extension to override the new tab behavior.