The default install of Ubuntu lacks an emoji picker. I found that the best option similar to Window’s neat emoji picker is Emote.
$ sudo snap install emoteKeyboard shortcut: The default keyboard shortcut Ctrl + Alt + e is supposedly how you launch this app. However, this keyboard is not registered on Ubuntu/Wayland. But, adding this keyboard shortcut is easy following the steps here. Since I switch between Windows and Linux a lot, I used the Win + . keyboard shortcut instead for this.
Usage: After the picker is launched, type the description of the emoji and pick the emoji. The picker disappears and the emoji has been copied. Use Ctrl + v to paste the emoji in any app.
Tried with: Emote 4.0.1 and Ubuntu 22.04