When using zsh as the default shell the snap icons do not appear to show in the menu by default (KDE Plasma and Ubuntu 20.04, 20.10 and 21.04).
To fix this, edit /etc/zsh/zprofile and add the following line to the bottom:
emulate sh -c 'source /etc/profile.d/apps-bin-path.sh'
On Ubuntu 22.10 onwards an additional change needs to be made otherwise some/all snaps will not be able to be opened from KDE.
Create the file ~/.config/plasma-workspace/env/snap.sh with the following content:
export XDG_DATA_DIRS="$XDG_DATA_DIRS:/var/lib/snapd/desktop/"
Make the file executable:
chmod +x ~/.config/plasma-workspace/env/snap.sh
Reboot and the snaps should be working as expected.