As an aside, I think you could get a smart plug that would support a 15 amp load that could give you a notification if the load went away. Might not be perfect, but just reading about having a relationship with a washing machine in a theoretical, second-party kind of sense makes me angry :)
Setting up home assistant to send push notifications via Smart plug amperage changes sounds like a great way to begin a long term committed relationship with your appliances
Edit: what the other guy said. I have a diver watch I just spin the dial to see how much time has passed since I started something. One time at the height of my Arduino hackery I didn't have a tea kettle and just boiled water in a sauce pan and said to my roommate, I bet I can shine a laser on the surface of the water to detect when it's boiling and make a noise, she laughs and says congrats you've invented a more complicated whistling kettle. Really humbling experience.
My washer has this 'Eco' mode, that is supposed to optimize time, water, and energy usage based on load weight and how dirty my clothes are. It finishes anywhere between 30 to 50ish minutes. Same settings an d all.
No, not at all. It's not really possible unless you're using an extremely basic washer with no spin (Or a very poor spin) cycle. A lot of the reason washers are terrible at estimating how long a wash cycle is going to be is because they spend a variable amount of time balancing the clothes before the spin cycle.