I have two MPP 6048's now, but started a couple years ago with just one, paired with just one 100Ah server rack battery.
Internally each MPP6048 is really just two 3kW inverters side by side.
This is how they can supply 120 & 240 with just a single unit, each 3kW inverter is making 120 volts, just 180-degrees out of phase with each other. To my understanding this is not the same as systems that rely on an auto-transformer, which if it cuts out, the result is 240vAC where 120vAC should be. Ian has a good video on this issue and the consequences.
With just one 6048 I found it was touchy to run/start a high load on a single phase, with nothing (or nearly nothing) on the other phase. ie, trying to start my funace fan on L1 (120vAC) while there was literally zero load on L2 a single MPP6048 went into fault on 'out of balance load'. I was able to 'fix' this by just putting my shop lights on L2 to reduce the out of balance. Each 6048 has a max output of 27.3A total, based on the loads you describe, I can imagine the front load washing machine may have been turn on about the same time as your fridge did a cycle, and if these are both on one leg (ie say both these are on L1) then the start up surge may have been too high. This may never have happened during the first two years you have used the equipment, since it is just chance the fridge and washer both start at the same time, or Fridge running a cycle just as the washer was started. It is not just chance to have two large loads on the same leg (ie L1) this can be changed in the electrical panel so the two are split to L1 and L2.
The MPP have an internal relay that closes during inverting (running on battery) I wonder if this relay got cooked/overloaded.
I learned ealy on, and it is in the MPP manual that the 6048 needs at least 200A available from battery. My first set up only had 100A battery, and this caused issues with larger loads, like seeing the vAC drop below 120 during starting a motor (like a large fridge compressor). When I added a second 100A rack battery, this issue never happened again. You don't say how large the battery pack you are using is, perhaps it can't supply 200A to the inverter, which dropped the voltage, which increased the amperage and blew up something. This shouldn't happen, in my experience with my units, they will shut off power if overloaded, beep warnings, and turn on red fault lights, maybe trip the reset breaker on the bottom of the unit near the AC output.