This indeed appears to be a significant flaw with how TLS is set up for the "Data to server" functionality (for e.g. Modbus to MQTT forwarding). There is a silly though straightforward workaround:
You can generate a dummy (but valid) combination of certificate and key, e.g. from https://www.selfsignedcertificate.com. Use those as the client certificate and key in the configuration, along with the broker's CA certificate. This worked for me, against a Mosquitto broker using a self-signed certificate (but no two-way certificate auth).
I'm not sure whether service logs are available anywhere, but you can test the connection manually, by running:
on the router (preferably after temporarily disabling the actual "modbus_data_sender" service, to avoid two identical processes running simultaneously).
First the configuration is printed out, and after that if the connection to the broker is successful, you'll get the message
Sender cfgxxxxxx_xxxxxxxxxx is running through a loop
followed by collection and transmission of Modbus data. If there is a connection issue, you'll likely get
Failed to connect
or similar. Finally, if insufficient certificates have been supplied (e.g. you didn't actually provide a client cert and key), you'll probably get
skipping: bad CA file / certificate / key file