How Do I Completely Remove XFCE After Installing MATE

Well the title say it all how do I fully remove XFCE from Debian after installing MATE?
I have tried the following commands in terminal.
sudo apt remove xfce4
sudo apt remove xfce4-session
sudo apt autoremove
these have mostly worked but I still have some lingering desktop icons related to XFCE.

I had also tried the below commands afterwards but they didn't remove anything further
sudo aptitude purge xfce-desktop    didn't work
sudo apt autoremove 'xfce4'            didn't remove anything further
sudo tasksel remove task-xfce-desktop     didn't remove anything further
sudo dpkg -P xfce                           didn't remove anything further

Has anyone removed XFCE after installing a different desktop environment?
Or is the answer just do a fresh install of Debian 12.4 with only Mate selected
and install linuxcnc uspace afterwards?

This might help.
mxlinux.org/wiki/xfce/how-to-completely-remove-xfce/

Are you sure that the lingering icons belong to xfce and not ones you put on there?
I didn't think XFCE put stuff on the desktop.

I should clarify. It leaves XFCE terminal and a few others in the menus. When I get done at work I will write down the exact ones I can find
and where they are located. That said if the work around is as tommylight has said install the Mate iso and install linuxcnc from there so be it.
On the plus side it bypasses the current problem (as of 2-8-2024) of the raspi-firmware inadvertently being installed as well.