After hours of confusion/scrambling/asking friends, here's the culprit: a recent update to apparmor breaks them.

Here's a link to the bug, which also includes a workaround:
https://bugs.launchpad.net/ubuntu/+source/apparmor/+bug/2072811

Here's the very simple workaround itself:

sudo aa-disable /usr/bin/bwrap

(If you don't have aa-disable, install apparmor-utils first)

Phew. Oh my god. What the fuck,