How does logrotate exactly handle "daily"?

I believe it's the content of the state file, which is my case is /var/lib/logrotate.status. Each file has one line, which is the date on which it was last rotated; if you run logrotate on such a date that a given file is due for rotation, given the number of days between current date and the date in the file (1 for daily, 7 for weekly, etc.), the file will be rotated.

logrotate doesn't seem to care at what time of day it's run; even if it usually runs at 2355, if you were to run it at 0130 instead, it would still rotate files marked daily and last done yesterday; but having done so it would put today's date into the state file (against any rotated files), so a second run at 2355 would do nothing.

From the logrotate man page:

Normally, logrotate is run as a daily cron job. It will not modify a log more than once in one day unless the criterion for that log is based on the log's size and logrotate is being run more than once each day, or unless the -f or -force option is used.

It runs on crontab schedules. You just need to find which crontab schedule has logrotate configured. Normally, it's in the daily /etc/cron.daily/. The generic crontab schedules are available in /etc/crontab.

Sample below:

# run-parts
01 * * * * root run-parts /etc/cron.hourly
02 4 * * * root run-parts /etc/cron.daily
22 4 * * 0 root run-parts /etc/cron.weekly
42 4 1 * * root run-parts /etc/cron.monthly```