I assumed that it would be listed as something like gnome-mail, but I have combed through Synaptic and haven’t found a “Mail” app comparable to “Contacts”, “Files” etc. New to both Budgie as well as GNOME 3, so I am a bit lost.
The email app the full client ships with on 20.04 is geary. In 21.04 the community has chosen thunderbird as the default email client.
The list of packages we ship with on 20.04 is here https://bazaar.launchpad.net/~ubuntubudgie-dev/ubuntu-seeds/ubuntu-budgie.focal/view/head:/desktop