And I found the solution:
AllowedIPs = 0.0.0.0/0, ::/0
works. All traffic is routed through Wireguard.
AllowedIPs = 192.168.23.0/24, 0.0.0.0/0, ::/0
only routes local traffic through Wireguard but the rest over the standard internet connection.
The checkbox to route all traffic through Wireguard must also be checked.