I suspect that Benjamin has xul-ext-gnome-keyring installed, with which Thunderbird 60 broke compatibility; see:
"xul-ext-gnome-keyring doesn't work with firefox >=57" <https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=881506> The assertion there, "In the meantime this still works for firefox-esr" from December 2017, is of course no longer true that 60 has become esr; and while there's not yet any mention of *Thunderbird* in that bug, it does appear to be the same sort of problem due to Thunderbird 60 having made similar motions to phase out the XUL extension mechanisms-- which I guess is already known, seeing the notes in the Debian changelog like this: * [4a993c5] adding additional packages to Breaks with thunderbird The packages calendar-exchange-provider and enigmail xul-ext-sogo-connector aren't compatible to the webextension interface and we need to add a versioned Breaks. I had the same problems as Benjamin described with a GMail account, but *also* had a similar "Thunderbird just never completes login" problem with an Dpvecot IMAP server that I administer (also on Debian). After removing the xul-ext-gnome-keyring package, Thunderbird 60 works with both accounts :) I guess the thunderbird package should add xul-ext-gnome-keyring to its "Breaks" list?