The canonical (no pun intended) way to upgrade from the deb package to the snap package, is to
install the snap package
run sudo lxd.migrate, which asks you to uninstall for you the LXD packages (both server and client).
If you want to remove LXD manually, then you need to run the following. The following autoremoves any LXD dependencies, and this includes the lxd-client package.
sudo apt remove --purge --auto-remove lxd
The problem you got is that you did not remove the lxd-client deb package, therefore the binary /usr/bin/lxc takes precedence in the $PATH over the binary /snap/bin/lxc.