I have it working now. I tested it on a fresh installation.
The issue was resolved by installing the 'xauth' command:
sudo apt-get update
sudo apt install xauth
After installing 'xauth', RDP connections from Windows worked as expected.
I'm not entirely sure why this fixed the problem, but my hypothesis is that 'xauth' is required to add the authorization information used to connect to the X server and stored in the '.Xauthority' file.
unspecified's post in Armbian 22.11.4 - Root (RDP) Remote Desktop Working - Non Root User not working was marked as the answer