Does the freezer light go out when the freezer door switch is manually operated, you didn’t say.
If so then the freezer door switch is OK.
Check that it is the same for the refrigerator compartment. Looking at the wiring diagram the refrigerator compartment has two door switches, left and right. However when searching for the location of the refrigerator door switch locations using the parts diagrams there are only 2 door switches shown, one for the freezer and only one for the refrigerator.(Scroll right to find the Wiring Information diagram along with the other parts diagrams).
The door switch has basically two functions. Signal the control board to turn on/off the light and to turn off/on the evap fan when a door has been opened and closed. (as long as the compressor is running)
If all the switches work OK when manually operated i.e. appropriate light turns off then it is looking like a control board problem.
If operating/releasing one of the door switches doesn’t affect the operation of its light then maybe check that the door switch is working OK electrically when operated and released by testing it with an Ohmmeter. Do this with the power disconnected from the refrigerator as AC line voltage goes through the switches.
The circuit shows that the refrigerator door switch is a changeover switch (part #19 - ref light/water tank/filter valve parts diagram) so there should be continuity through one set of its contacts when operated and through the other set when it is released and that the freezer door switch is just a break switch i.e. has continuity when released (part #4 - frz light/evaporator/evap fan assembly parts diagram). Apologies if you know how to test switches etc