Thousands of images suddenly became unpublished. All the galleries exist, all the images are in the database, but they are all not Published.

Is there a quick way to set all images in every gallery to published?

Activate the `publishContent` plugin.
Then go to Admin > Overview > click the `publishContent` button.
You'll see all un-published items and you can select all items to be published.

publishContent doesn't appear to be an option. I have Zenphoto version 1.4.2 [8956] (Official Build) and it is not listed.

Is there anyway I can add the plugin?

Yes, upgrade to the current version Or at least 1.4.3 where it was added (around four years ago). But note we can only support the current version.

From the overview page when I check for updates it responds with "You are running the latest zenphoto version."

I'll download and upgrade...

Updated to version 1.4.11 and with the publishContent plugin everything is back up and running.

I see the "check for updates" button has been removed!

From the overview page when I check for updates it responds with "You are running the latest zenphoto version."

Your version was so old that the check did run empty as it had been changed meanwhile ;-)

I see the "check for updates" button has been removed!

Not exaclty, it is part of the check for update plugin currently ;-)