Hi, @psion13 (Aaron Flora) 
To try to help you, I've just done the following and I'm happy to say that it worked:
1. - In the, let's call it, "Server" machine running Ubuntu MATE 24.04 LTS ("Noble Numbat"):
1.1. - Install the "xrdp" package:
sudo apt install xrdp
1.2. - Create an .xsession file directly in the "home directory" of your user with the following lines:
unset DBUS_SESSION_BUS_ADDRESS
unset SESSION_MANAGER
mate-session
By the way, about this idea of creating an .xsession file with the above lines, all credit goes to @OldStrummer (Fred) for his following reply in another older topic:
2. - In the, let's call it, "Client" machine running Ubuntu MATE 24.04 LTS ("Noble Numbat") or an earlier version:
2.1. - Install the "Remmina" RDP (Remote Desktop Protocol) client:
sudo apt install remmina
2.2. - Use "Remmina" to access the IP address of the Server machine using RDP
I hope this helps Please tell us if this solution also works for you or not.