Where to find logs/information about unattended-upgrades (apt)?

Unattended upgrade has its own log-file in /var/log/unattended-upgrades/unattended-upgrades.log

It is policed by anacoron.

# These lines replace cron's entries
1   5   cron.daily  run-parts --report /etc/cron.daily
7   10  cron.weekly run-parts --report /etc/cron.weekly
@monthly    15  cron.monthly    run-parts --report /etc/cron.monthly

/var/log/dpkg.log also /var/log/apt/history.log

Both those log files contain timestamps and descriptions if action was taken. if no action was taken there is no log.

automated updates runs from /etc/cron.daily/apt and /etc/cron.daily/* runs from /etc/crontab in the early morning.