Also: I had a VM, set up with Debian unstable and XFCE, which I just updated yesterday. Prior to updating, Synaptic launched from the menu system without issue; after updating, I see the same behavior as on my laptop, for which I filed the bug. The VM had updated to policykit-1 0.105-17.
Both systems use the XFCE interface and have sudo configured.
Synaptic is the application where I first noticed the issue, but I'm fairly sure it's not a Synaptic issue per se. I get the same error message if I execute 'pkexec whoami', for instance.
A few months ago, I'd had Debian stretch, with XFCE, on that laptop. After a few weeks, I had what seemed to be the same issue I'm seeing now. Unfortunately I'd wiped the laptop in between and so don't have any logs.
From what I've seen from some bug searches and general Web searches, there are a fair number of reports of applications that require authentication failing to launch from the menu system after an update, but working fine when launched from the command line with sudo. Synaptic is mentioned most often, including similar errors involving 'synaptic-pkexec' at the command line. None mention fixes, but a few mention the problem goes away again after an update. A lot of them mention XFCE, but I don't recall any other desktop environments mentioned.
policykit-1 was my best guess about where the problem lies. Please let me know if there's anything further I can do to assist in troubleshooting.