> the default keyboard shortcut for the emoji picker on GNOME/GTK is ctrl-. (same as the Firefox shortcut).

Hmm, I wonder how new that is? Could be possible that my GNOME installation is old enough to predate that, and they didn't overwrite the config like Firefox did? Because I've been using Firefox + 1Password + GNOME for years, and for as long as I can remember, `ctrl + .` has opened 1Password dialogue in Firefox, and I'm not sure I've ever seen an Emoji picker in GNOME, although I know it exists somewhere.