The shelly 1 is inexpensive and can absolutely be used as a momentary button controller out of the box (an advertised use case is garage door opener). For power sensing you will need something that monitors the input power - perhaps an Eve energy plug?
Home Automation
Discussion about general home automation ideas and projects, home automation protocols like Z-wave, Zigbee, Matter, etc, and home automation software and hubs like HomeSeer, Home Assistant, OpenHAB, Homey.
My concern is that the Shelly won't be able to tell if the ice machine is on or off. The automation would be something like "toggle the ice machine" vs "turn the ice machine on".
If there is some way I could wire a Shelly sense pin to the ice machine controller and tell it to use that to tell whether toggling would turn it on or off. IDK
The ice maker will have a dramatically different power draw if it is on or off. The Eve energy plug can monitor its draw and you can write logic to differentiate on/off. The Shelly can turn it off or on based on your needs.