I found it the hard way.

My database is rather small. It’s actually less than 20 Mb in total. That’s of course, if I exclude the 1.4Gb of data that I have in wp_options alone. Most of if being transients. Most of which have expired some time ago.

I’ll spare you the story of how I came to the conclusion, but will skip straight to it:

If the whole site is hiden behind a basic authentication (htpasswd) wall, then there is a very good chance the wp-cron will not be running. And if it’s not running, it will not run the process for deleting expired transients, which would lead to causing the database clogging.