yeah, you are using DHCP and this is taking to long for the Ethernet interface to complet configuration
1st attamed to configure IP address is not successful. Looks like the DHCP server is taling to long to offer an IP address
Sep 23 20:20:58 RaspberryPi-4 ifup[418]: DHCPDISCOVER on eth0 to 255.255.255.255 port 67 interval 5
Sep 23 20:21:03 RaspberryPi-4 dhclient[418]: No DHCPOFFERS received.
Sep 23 20:21:03 RaspberryPi-4 ifup[418]: No DHCPOFFERS received.
Sep 23 20:21:03 RaspberryPi-4 ifup[418]: No working leases in persistent database - sleeping.
Sep 23 20:21:03 RaspberryPi-4 dhclient[418]: No working leases in persistent database - sleeping.
However the system belive there is a valid interface 
Sep 23 20:21:03 RaspberryPi-4 systemd[1]: Finished ifup for eth0.
Sep 23 20:21:03 RaspberryPi-4 systemd[1]: Reached target Network.
Sep 23 20:21:03 RaspberryPi-4 systemd[1]: Reached target Network is Online.
In meantime Wireguard is trying to start, which is failing as no eth0 interface has been configured until now
Sep 23 20:21:03 RaspberryPi-4 systemd[1]: Starting WireGuard via wg-quick(8) for wg0...
...
Sep 23 20:21:04 RaspberryPi-4 systemd[1]: wg-quick@wg0.service: Failed with result 'exit-code'.
Sep 23 20:21:04 RaspberryPi-4 systemd[1]: Failed to start WireGuard via wg-quick(8) for wg0.
And finally, your system is getting an IP address assigned. But to late for Wireguard.
Sep 23 20:21:05 RaspberryPi-4 dhclient[418]: DHCPDISCOVER on eth0 to 255.255.255.255 port 67 interval 7
Sep 23 20:21:05 RaspberryPi-4 dhclient[418]: DHCPOFFER of 192.168.1.80 from 192.168.1.90
Sep 23 20:21:05 RaspberryPi-4 dhclient[418]: DHCPREQUEST for 192.168.1.80 on eth0 to 255.255.255.255 port 67
Sep 23 20:21:05 RaspberryPi-4 dhclient[418]: DHCPACK of 192.168.1.80 from 192.168.1.90
A workaround could be to use STATIC IP address instead of DHCP. If possible, create an IP address reservation on your router for your IP 192.168.1.80. Once done, switch to STATIC IP on your DietPi device. You should be able to use the copy function on the STATIC configuration menu. This way you assign the very same IP address information on STATIC you have been using before on DHCP.
If all goes well, you could reboot your system and check WireGuard again.