I’m back, with no good news.
I’ve tried deactivating all plugins (except Akismet) and falling back to the default Kubrik theme, to no avail.
As explained above, comments are present in the database, in the back-end, and in the front-end when clicked on the permalink, but it’s the comment counter that seems faulty, displaying zero about 99% of the time.
I’ll be really thankful for any suggestions!