I have a Wireguard VPN to my home network and there it works exactly like you tried it. Connect to VPN, then use the internal IP to connect to the service. Maybe there are settings in the server or client that prevent that. For example, you can set specific IP ranges to not be routed through the VPN (so you can access a local service in Network A even though you are connected to VPN B).

I’m no network expert, but maybe some additional information about your setup can help other user help you better.