Yes, byzantium is broken.
Debian’s associated error report is: #956910 - gnome-shell: System hangs with GnomeDesktop:gnome_bg_slide_show_set_property: assertion failed: (GNOME_BG_IS_SLIDE_SHOW (object)) - Debian Bug report logs
This is a known transitional problem during the upgrade from GNOME
Shell and gnome-desktop3 3.34.x to 3.36.x. It will be resolved when
the transition finishes (probably sometime in the next 1 to 2 days),
but there is nothing that the maintainers of individual packages can do
about it right now.
Besides downgrading / frankendebian hacks, there seems nothing to be done but waiting for the upstream situation to resolve itself and PureOS taking it over. Tried the same (switch to lightdm) to no avail. Kind of annoying but a risk of the bleeding edge, I guess.
For now I managed to set the terminal font to a huge size (using instructions here: How do I change the font or the font size in the TTY (console)? - Ask Ubuntu) to make it readable at all on a 4k monitor and am using Linux old-school style 