Firefox currently acts as a search provider, allowing web search and tab/history search from gnome itself, but there are a few issues with the implementation. While I am not a developer, I think the proposed solutions should be implementable given GNOME web's similar search provider or at least included as options in about:config.
- Its availability depends on package format and distribution. I think there were some reddit threads, but I cannot find them after the Reddit API protests. It works on Fedora 38 with the RPM, and there is some convoluted configging to make it work with the Fedora Flatpak.
- It only works when Firefox is open. By contrast, GNOME Web/Epiphany has a near-identical implementation but still works when Epiphany is closed (not running in the background).
- Link opening is inconsistent. Web searches launch in a new window after a moment of delay, whereas history results open in a new tab in the last active window.
My personal preference is for both to open in a new tab in the last active window and only open in a new window if Firefox was closed. Again, this should be doable as GNOME web and Firefox both have the functionality to open a new tab in the last active window.
Links/Sources: