Comment 12 for bug 1830070

purging gdm* also removed ubuntu-desktop - so you wouldnt be able to run the second sequence of commands.

anyway - I followed your instructions on a fresh ubuntu iso fully upgraded - installed ubuntu-budgie-desktop and then purged gdm3 and ubuntu-desktop.

budgie-desktop-settings started successfully - tested logout/reboot as well.

So sorry - it must be something else that you have removed at some point.