The solution that eventually worked was: as shown below. What made the difference is point 3, I only included the rest because it's unclear from the post itself what the final setup is.
1- Reinstalling Nouveau with
sudo apt install nouveau-firmware
2- Re-enabling the Additional Drivers;
3- Replacing the current display manager (SSDM) with XDM:
sudo apt install xdm
The terminal should automatically display a menu asking you which display manager to use, and you simply need to select XDM with the arrow keys and press the enter key.
4- Rebooting the computer.
Getting the Nvidia driver directly from their website did not work as it conflicts with Nouveau in a way that I could not figure out. If you let the Nvidia installer disable Nouveau, do:
rm /usr/lib/modprobe.d/nvidia-installer-disable-nouveau.conf
rm /etc/modprobe.d/nvidia-installer-disable-nouveau.conf
Amazingly, this seems to also have fixed the other issue I mentioned at the very end of my post.
Thank you to Mika Lindqvist and u/wxl on Reddit for the invaluable help!