Every repo was giving signature errors in apt:
Err:6 http://security.debian.org stretch/updates InRelease
At least one invalid signature was encountered.

This was pretty recent. My updates in May were fine.
This ONLY affected apt* update. Not clean, install, purge, etc.

I could bypass the error by telling the sandbox to become root:
apt -o APT::Sandbox::User=root update

/tmp was still 1777. I did find /var/tmp was linked to /tmp, which killed dovecot install.
No idea why that’s a problem, because my /tmp is persistent across reboots.
A snotty developer somewhere indicated it was the end of the universe.
Now, /var/tmp is just part of /var. Whatever.

So, someone did a hard cleanup of cache, and that fixed it for me:
sudo apt-get clean
sudo mv /var/lib/apt/lists /tmp
sudo mkdir -p /var/lib/apt/lists/partial
sudo apt-get clean
sudo apt-get update

Then I compared /tmp/lists and /var/lib/apt/lists.
Exactly the same for everything, except top level permissions.
The old one was 755 and the new one is 750.

WTF?!?!? Why do we care if “other” can read the package lists?
There is ZERO sensitive data in there?

I decided someone was intoxicated, watching Rick and Morty, making out with their significant other, and coding with their non-dominant hand, just to see if they could maintain focus on a dare.