I have:

ENABLE_AMAVIS=1
ENABLE_SPAMASSASSIN=1

But somehow, spamd doesn't seem to run at all.
I don't find any spamd log files under /var/log/ either.

Does it run in a different way in this mailserver?

sa-update works fine, but,

root@srv:/# /etc/init.d/spamassassin reload 
Reloading SpamAssassin Mail Filter Daemon: No spamd found running; none killed.

root@srv:/# ps aux | grep spam 
root      2857  0.0  0.0   3164   708 pts/0    S+   17:40   0:00 grep spam

If I run /etc/init.d/spamassassin start,
spamd starts successfully and stays active.

But if I restart the container, it doesn't seem to be active after.

Please note that the cronjob at /etc/cron.daily/spamassassin runs /etc/init.d/spamassassin reload after an update, but if spamd isn't running, then it doesn't start either.