One) while it’s true that the Logitech Harmony will consider this an entertainment device and you can only have one entertainment activity going at one time, there is an official logitech workaround for this. It’s clunky to set up, but it does work. Basically you have to add it to every activity you have, set it up to not turn off as you’re shifting between activities, and then have one more activity to turn it on.
See the following:
this has Alexa integration. Because of that, there is yet another hacky work around. You can have A different device speak an instruction to an echo device and automate it that way. Like I said, it’s pretty hacky, but it does work.