USB to RS485 Converter Industrial Adapter Original FT232RL and SP485EEN Fast Communication Embedded Protection Circuits Resettable Fuse ESD Protection

It's probably RS485 over RJ45.I have solar batteries/inverters that use these connectors for that purpose. You could probably plug in something like an RS485-to-USB adapter or a waveshare box to sniff the traffic on it.It'd probably be possible to add it to something like Home Assistant and get a notification on your phone when the wash cycle is done.