Sometimes sudden shutdown after serverstart followed by automatic restart after about 5 Minutes

I wake up my homeserver via wake on lan. Most of the times, after about 45 seconds I can hook into the machine with ssh. That is perfectly fine. It appears, that when the last log in was a longer time ago (a couple of hours), I can not access the server right away after about 45 seconds. I have to wait about 5 more minutes to be able to get in. I do not find any hints in /var/log/. Here is what I can observe:

ME@Laptop:~$ date
Wed 29 Dec 2021 07:04:57 PM CET

ME@Laptop:~$ wakeonlan 17:F2:42:54:04:A6
Sending magic packet to 255.255.255.255:9 with 17:F2:42:54:04:A6

ME@Laptop:~$ ping 192.168.0.201
PING 192.168.0.201 (192.168.0.201) 56(84) bytes of data.
From 192.168.0.22 icmp_seq=1 Destination Host Unreachable
From 192.168.0.22 icmp_seq=2 Destination Host Unreachable
...
From 192.168.0.22 icmp_seq=35 Destination Host Unreachable
From 192.168.0.22 icmp_seq=36 Destination Host Unreachable
64 bytes from 192.168.0.201: icmp_seq=38 ttl=64 time=8.96 ms       <--- There it is shortly
From 192.168.0.22 icmp_seq=78 Destination Host Unreachable         <--- ... and gone!
From 192.168.0.22 icmp_seq=79 Destination Host Unreachable
...
From 192.168.0.22 icmp_seq=361 Destination Host Unreachable
From 192.168.0.22 icmp_seq=362 Destination Host Unreachable
64 bytes from 192.168.0.201: icmp_seq=363 ttl=64 time=1352 ms
64 bytes from 192.168.0.201: icmp_seq=364 ttl=64 time=329 ms
...
64 bytes from 192.168.0.201: icmp_seq=389 ttl=64 time=2.03 ms
64 bytes from 192.168.0.201: icmp_seq=390 ttl=64 time=4.15 ms
^C
--- 192.168.0.201 ping statistics ---
390 packets transmitted, 29 received, +273 errors, 92.5641% packet loss, time 1100ms
rtt min/avg/max/mdev = 1.714/62.398/1352.149/250.840 ms, pipe 4

ME@Laptop:~$ ssh S02
ME@s02's password: 
Linux S02 4.19.0-18-amd64 #1 SMP Debian 4.19.208-1 (2021-09-29) x86_64

The programs included with the Debian GNU/Linux system are free software;
the exact distribution terms for each program are described in the
individual files in /usr/share/doc/*/copyright.

Debian GNU/Linux comes with ABSOLUTELY NO WARRANTY, to the extent
permitted by applicable law.
Last login: Wed Dec 29 11:28:52 2021 from 2001:4dd7:2e8c:0:61de:9f:e12f:ba74

ME@Server:~$ sudo shutdown now
[sudo] Passwort für ME: 
Connection to s02 closed by remote host.
Connection to s02 closed.

ME@Laptop:~$ ping 192.168.0.201
PING 192.168.0.201 (192.168.0.201) 56(84) bytes of data.
^C
--- 192.168.0.201 ping statistics ---
12 packets transmitted, 0 received, 100% packet loss, time 262ms

ME@Laptop:~$ date
Wed 29 Dec 2021 07:12:53 PM CET

ME@Laptop:~$ wakeonlan 17:F2:42:54:04:A6
Sending magic packet to 255.255.255.255:9 with 17:F2:42:54:04:A6

ME@Laptop:~$ ping 192.168.0.201
PING 192.168.0.201 (192.168.0.201) 56(84) bytes of data.
From 192.168.0.22 icmp_seq=1 Destination Host Unreachable
From 192.168.0.22 icmp_seq=2 Destination Host Unreachable
...
From 192.168.0.22 icmp_seq=38 Destination Host Unreachable
From 192.168.0.22 icmp_seq=39 Destination Host Unreachable
64 bytes from 192.168.0.201: icmp_seq=40 ttl=64 time=493 ms          <--- There it is and it stays on!!!
64 bytes from 192.168.0.201: icmp_seq=41 ttl=64 time=1.67 ms
...
64 bytes from 192.168.0.201: icmp_seq=264 ttl=64 time=2.09 ms
64 bytes from 192.168.0.201: icmp_seq=265 ttl=64 time=2.82 ms
^C
--- 192.168.0.201 ping statistics ---
265 packets transmitted, 226 received, +39 errors, 14.717% packet loss, time 512ms
rtt min/avg/max/mdev = 1.631/5.289/493.460/32.711 ms, pipe 4

ME@Laptop:~$ date

How is it to explain that my system dies suddenly. How is it to explain that it restarts itself magically after about 5 more minutes? Where can I possibly look to find out what is happening? I strongly assume, that it is not a temperature problem, since it only happens, when I start the machine cold after some hours. By shutting down manually and starting right after the unwanted restart there seems to be no problem any more.