Since I like to use bemenu I just wrote the derivation myself, it's super short and simple especially borrowing from the build.sh script in wofi-emoji repository. You can get the emoji data like so:

emoji-data = pkgs.runCommand "emoji-data" {
        buildInputs = [ pkgs.cacert pkgs.curl pkgs.jq ];
        outputHashAlgo = "sha256";
        outputHash = "sha256-znAwFu0vq2B7lQ8uvG0xKv9j3jYr6P0CZpjoKMNPhZw=";
      } ''
        curl 'https://raw.githubusercontent.com/muan/emojilib/v3.0.6/dist/emoji-en-US.json' \
            | jq --raw-output '. | to_entries | .[] | .key + " " + (.value | join(" ") | sub("_"; " "; "g"))' \
            > $out
      '';

And then write a small wrapper script of your liking. I'm using wtype and bemenu, but you could just as easily use wl-clipboard and rofi for instance. This is to me one of the huge benifits of nix, how you can slam these small scripts together and not worry about missing dependencies when taking the configuration to other systems.