I have “fixed” the problem just by reinstalling and activating the plugin. Now error_log isnt getting 1 GB big in minutes.
But I guess the whole problem isn′t fixed yet. On CPanel I see the I/O usage is at its limit. The error_log was growing with warnings saying a file wasnt found on the server. Now Dropbox Backup & Restore is making an unwanted local backup of the site.
I will wait until it finishes making this backup copy, as stopping it now would probably cause the same problem again. I will report back then, to see if it gets fixed that way.