I've now uninstalled and re-installed (and re-did all of the settings, and re-built the index).
And the error is now gone.
In my case, the problem might have happened because I keep the code under source control, and so I *might* have upgraded on the main site, and not on this site, and then run my database sync shell script and not updated the files properly. I think I've always updated all of the plugins before doing the sync, but it is possible that I missed it, and so then might be entirely my fault. I'll keep an eye on it, and make sure to always upgrade both sites' files before syncing the database.