It successfully writes the routes, but when I do a tracert, then the traffic doesn't go through the VPN server.
There is no logic. If trafic is no going thru the tunnel, then routes are not write.
Verify that OpenVPN is started with elevated rights.
I am using server-bridge mode, so the IP is given from the local network's (router's) DHCP server.
DCHP is on what side - server or client LAN?