Firefox has a long history of Gtk desktop integration. We use native Gtk3 theme to style widgets, we try to use system colors where it’s possible, honor global dark themes and so on and we feel that the application should play nicely with the rest of the system.

Plasma/KDE users may admit that Firefox is a GTK application and KDE integration is missing as well as integration for various tiling windows managers. This isn’t an intention but merely a lack of manpower to code and maintain that.

Another step in the Gnome integration effort is to provide a global search experience by Firefox. It’s already available in Fedora by default by downstream patches but the patches were integrated upstream so they’re available for all users of Mozilla stock builds since Firefox 78 (that also includes recent ESR line).

Firefox GNOME Search provider can be enabled in three easy steps:

• Install Firefox desktop and Firefox search provider files. You can use prepared ones from Mozilla or create your own. Copy firefox.desktop to /usr/share/applications/ and firefox-search-provider.ini to /usr/share/gnome-shell/search-providers.
• Run Firefox, go to about:config and set
  browser.gnome-search-provider.enabled to true.
• Restart Firefox.

Now, when Firefox is running, you should see search results when you hit ‘Super’ key in Gnome and type something. If you don’t get anything, check:

• Is D-Bus service running? Use D-Feet tool to inspect if Firefox provides org.mozilla.Firefox.SearchProvider interface on Session Bus.
  
• Are Firefox search results shown? If not, go to Gnome Settings -> Search and look for Firefox. If the Firefox is missing in search engines, your firefox-search-provider.ini isn’t properly installed. To see Firefox search results, move Firefox up to the top.