(UPDATE: Back when I needed this, Ubuntu 19.10 was not listed under Quick Create. This, however, has changed. I would recommend using Quick Create, if possible, over my solution I provide below.)
I fixed the problem myself. Unsurprisingly, Gnome turned out to be a problem. Since I am not a fan of Gnome, I did not bother to make Gnome work with xrdp. Since xrdp is a necessity to get EnhancedSession to work, I chose an alternative desktop environment: Mate.
I reinstalled Ubuntu using the server iso in order to have more control of what gets installed and what not. While the server iso is nice for finding the source of the problem, I would not necessarily recommend it. Just choose a flavor of Ubuntu using something like mate or xfce.
Once you have a Gnome-free Ubuntu 19.10 with an alternative desktop environment that plays nice with xrdp, you need to download the following script:
Extract the content of the zip file and mark it as an executable (IMPORTANT!). Run it as root (with sudo). Reboot once the script has finished. Run the script again (also as root).
For completeness sake, I should mention, that I followed the following instructions to rid myself of Wayland: https://linuxconfig.org/how-to-disable-wayland-and-enable-xorg-display-server-on-ubuntu-18-04-bionic-beaver-linux
However, this should not be necessary, since the script has already dealt with Wayland, or at least it should according to the guy that modified it to work with Ubuntu 19.10.
Once the script has finished for the second time, do not reboot, like the script tells you, but turn the VM off.
Open PowerShell as administrator and enter the following line:
Set-VM -VMName <your_vm_name> -EnhancedSessionTransportType HvSocket
Do not forget to replace
<your_vm_name> with the name of your virtual machine.
I hope I did not forget any step that was necessary to get this to work.