As mentioned there is an OpenHab binding you can take a look at.
I started using OpenHab long before this binding was available so my setup is to use the OpenHab MQTT binding.
Technically it is quite simple, you seem to have all what is needed. OpenHab and Mosquitto can run on the RPi and a MySensors MQTT gateway sends the sensor messages to Mosquitto over your network. The Mosquitto passes all messages on to OpenHab.
Now my gateway is based on WiFi using a Wemos Mini or other ESP based board. I have also used an Ethernet MQTT gateway without any problems.
At the OpenHab side you need to create Items which listen to the MQTT messages and then the OpeHab rules can act on these messages and display results using the OpenHab sitemaps.
There is a lot of info available about how to set all this up so Google plus MySensors and OpenHab docs/forums will give you the details needed.
This rough description outlines one "manual" way of connecting to OpenHab. Also the serial gateway can be used but I think MQTT is the best option. I presume that the mentioned binding can simplify things but I have no experience of that approach.