Joulinar and jollyrogr, using STATIC IP might be faster but it doesn’t guarantee that the issue won’t happen then.
In my case adding
PreUp = /boot/dietpi/func/obtain_network_details
was required to start Wireguard after bootup in a STATIC IP scenario.
The error reminded me on this issue: Wireguard and static IP on RPi4 B (Github: WireGuard and Lighttpd not working after update to v6.26.3 · Issue #3175 · MichaIng/DietPi · GitHub)