I ran into the same issue on my Shelly 2.5. After some investigation of the cloud APIs and JavaScript i think this might be a bug and thus opened the following ticket T-20037569 with Allterco:
Myself and some other users (see Shelly 1 application and Input State (German)) ran into a strange bug where some of our Shellys (Shelly 2.5 in my case, Shelly 1 for other users from the linked threads) would not show the "Add input state identifier to the power button" checkbox in the "Application Settings".
I was able to investigate it and work around the issue (just for myself) by doing some browser devtool HTTP magic. I basically POSTed devices_data={"DEVICE_ID":{"input_state":true}} to the cloud /interface/device/bulk_update endpoint. From that point onward the "Add input state identifier to the power button" setting appeared and also stayed visible even when i disabled the option.
This leads me to believe this is actually a bug that occurs when the device is completely missing the input_state property (instead of it being either true or false) in the device entry returned by the cloud /interface/device/get_all_lists HTTP endpoint. Not sure under which conditions the device entry will end up in that state, but for me it occured on 1 of my 3 Shelly 2.5 devices. For another user it occurred on 5 of his 13 Shelly 1 devices.
I believe the actual bug in the code is in https://my.shelly.cloud/assets/js/modu…ice_settings.js in the init_input_state_events() function which does a "device.hasOwnProperty('input_state')" check. So if the input_state property is completely missing (for whatever unknown reason), the user will not be able to ever activate that option.
Obviously another option to fix this would be to make sure that the input_state property is always there (for the devices that support it).
I will try to keep you updated on Alltercos response.