It seems I’d misunderstood how the Plesk update cycle works.

Update #55, mentioned in the footnote in the question, was released on 3 June, but it was not installed on our server until 10 June (unlike update #56 which was released on 10 June but has not yet been installed). Part of update #55 is that PHP 7.2 is updated to version 7.2.19.

I just changed the PHP version from 7.2.19 to 7.1.30 in Plesk, which immediately fixed the issue, so clearly something is not right with the 7.2.19 version installed as part of the Plesk update.

It appears from various sources online – though not nearly as many as I’d have expected – that this is a general problem, not just limited to our server (e.g., [this WordPress forum answer](https://wordpress.org/support/topic/wordpress-5-2-9/#post-11624568) and [the end of this Plesk Talk question](https://talk.plesk.com/threads/wordpress-say-sql-server-is-too-old.352493/)). It’s a Plesk bug.