You can connect the "chassis GND" to your ground plane but then you lose the galvanic isolation which is one of the big advantages of Ethernet, IMHO. Raspberry Pi does this.
I had similar situation (100M ethernet, plastic case) and just left the chassis ground as its own small region under the connector, and quite obviously, with just plastic enclosure, it does not connect anywhere further. Was first-time pass in emissions and immunity, radiated and conducted and ESD. With 2.2ohm series resistors for edge rate control and 100M Ethernet compatible ESD TVS array. Did not test without these components.
I connected CHASSIS_GND to GND using two of the 2kV MLCCs just to reduce impedance.
Note the possibility of confusion: the bob smith termination network in itself contains a 2kV capacitor to CHASSIS_GND. This does not mean it has to be the only 2kV MLCC in the system. You can further connect CHASSIS_GND to GND with another 2kV MLCC, maintaining functional insulation (DC) between the grounds.