@Joulinar have you found a solution? I was not able to understand the reason why the command into root’s crontab is not executed.
I didn’t look for a solution. should I?
No, you should not, but maybe this topic could remain opened until solved?
I don’t see an issue with this crontab entry. Just did a very quick test on my RPi5 demo system and reboot has been triggered correctly using root user crontab.
Following has rebooted the system at 30 minute, and I guess it will reboot again within a hour 
30 * * * * /usr/sbin/shutdown -r now
thanks, i think it’s solved.