It has mysteriously begun to work for me....
Per https://github.com/flathub/org.gnome.Geary/issues/42 a workaround for this is adding explicit RW access to `~/Downloads` or similar, so at least people can print to PDF and print that using Evince or whatever.
Let's track this in bug #202363.
*** This bug has been marked as a duplicate of bug 202363 ***
Reopening since bug #202363 was resolved without fixing flatpak.
*** Bug 244332 has been marked as a duplicate of this bug. ***