Be careful which train you take. Only the IC trains on that route have the SBB restaurant and about half the trains are IR which don't. Also only some of the IC trains are a direct service. Several make one or two changes -- not much fun with a breakfast plate. Also the journey is short - less than an hour, so you will want to be sitting down in there asap.
Have a look at https://www.sbb.ch/en/station-services/during-your-journey/sbb-restaurant.html
You can also grab and go at the Migros or many other outlets in Bern station before you go up to your train and eat at your seat.
If you're going in the working week be advised that that route is very busy with commuters at what most would consider breakfast time. Check the train you're interested in for the number (1,2, or 3) of stick figures which will indicate expected use. They are usually pretty accurate.
The video on the link I gave shows no luggage facilities and no overhead racks in the dining car.