I figured out what happened.
When I go to:
https://jami.net/download-jami-linux/
... and click on the Trisquel logo, a one-click installer appears for
Trisquel 8.0, which correctly provides a .deb targeted at a 16.04 base. But
the manual instructions underneath tell me to add:
https://dl.jami.net/nightly/ubuntu_19.10/
It appears this is what I did, which I presume is why it's not working. If I
click the dropdown that specifies Trisquel 8.0, the manual instructions
change to give the correct URL:
https://dl.jami.net/nightly/ubuntu_16.04/
I've reported the problem here:
https://git.jami.net/savoirfairelinux/jami-packaging/issues/39
... and opened a separate forum thread for dealing with the problems
resulting from accidentally adding a 19.04 repo:
https://trisquel.info/en/forum/cant-install-jami-their-repo