Thanks for the great hint! 
I shall remember this!
A while ago, @flebourse kindly suggested there to set up the WG watchdog via crond, which I did:
# cat /etc/crontabs/root
11 6 * * 2 /sbin/rut_fota --fw_info >/dev/null 2>&1
* * * * * /usr/bin/wireguard_watchdog
There is further reading about WG watchdog (for other interested users, too). And in this thread, there is a more extensive crontab entry mentioned (and much more):
* * * * * /usr/bin/wireguard_watchdog' >> /etc/crontabs/root
/etc/init.d/cron restart
I do not know what the extra >> /etc/crontabs/root /etc/init.d/cron restart implies. Maybe @flebourse could explain a bit?
Following @Marija’s proposal, I see the below (and more, but please let me first stick to this):
# logread -f
17877 Tue Feb 25 17:15:00 2025 cron.err crond[10564]: USER root pid 3895 cmd /usr/bin/wireguard_watchdog
17878 Tue Feb 25 17:16:00 2025 cron.err crond[10564]: USER root pid 4196 cmd /usr/bin/wireguard_watchdog
In my case (just * * * * * /usr/bin/wireguard_watchdog), does cron.err really imply an error? How could I get details about this?
I will also follow your suggestions about further log reading and post results later.