Crash

Generally ESP works most efficiently during understeer / oversteer situations & or when braking / accelerating. If your vehicle aquaplained then the controls wouldnt kick in, or work effectively untill traction was restored, by which time you had probably hit the wall.

The airbags probably did not deploy because the vehicle didn't strike anything within the deployment parameters.

The electronic stability control (ESC) did not kick in because the computer for the ESC did not detect the skid, or the skid occurred so quickly that the vehicle passed through the window of opportunity where the system could recover the skid. You did not mention the condition of your tires, but if they were hydroplaning, there may not have been a differential in wheel speed, and/or the angle of the steering wheel was such that the computer thought the driver had the vehicle under control.

Is a major malfunction of the ESC and the air bag deployment system likely, since none worked during the accident?

No, since you did not get an SRS or ESC warning light prior to the accident.