It was caused by a broken library (libicuuc) that another member of the community noticed from my systemd boot journal output.:
May 22 15:27:53 dustinxps /usr/lib/gdm-x-session[3980]: /usr/bin/xfce4-terminal: error while loading shared libraries: libicuuc.so.70: cannot open shared object file: No such file or directory
I then used lddtree (pax-utils) to identify that vte3 was what was directly depending on it, which all of my terminals have in common. This jogged my memory that I had been prompted a couple of times regarding vte3 when I had upgraded and then confirmed the upgrade, but then it had stopped coming up. It then occurred to me that I had the transparency-patched version of gnome-terminal installed, and this likely caused vte3 to be built from source and depending on the old libicuuc. So, I needed to fully remove that version of gnome-terminal and vte3-git and all of its dependencies (maybe thirty packages, many of which seemed unnecessary). So, I did that, installed the pure vte3 binary package, reinstalled the dependencies, and reinstalled xfce4-terminal and gnome-terminal, and they now worked.
Good grief.