@Bernie_O, I have set the following:
apc.enable_cli=1
in /etc/php/7.0/fpm/php.iniand restarted PHP.
The same error persists in Nextcloud logs.
Upon further research, it seems those settings fit somewhere else.
I found this a tad confusing, as on first glance the PHP documentation seemed to indicate it goes into php.ini, but then I followed the instructions in this post NC13: "Memcache \\OC\\Memcache\\APCu not available for local cache" and appended the cli setting instead to /etc/php/7.0/mods-available/apcu.ini.
And now the annoying APCu CLI info entries into the log are gone. Yay! \o/