Thanks for your hints!
I used much simpler approach, which seems to work now. I only have owned a PHEV for two days though, so can't say I have yet very big experience with this.

But it has worked several times already.

Phone is old MotoG which I downgraded from Android 8.0 to Kitkat 4.4.4 to make the old "10 digit" mitsubishi app work. Then I removed lockscreen from settings, so phone always goes directly to Mitsu app when screen is enabled. Screen sleep timeout set to 1 minute so it stays lit through the operation, it doesn't seem to work if it goes blank.
Then, Tasker setup so that "Phone ringing from favorite contacts" triggers my task. So I can choose which numbers are allowed to start heating.
The task is like this:
1) End call (will signal "busy" to the caller, who then knows that at least Tasker was awake

)
2) Launch Mitsu app
3) AutoInput Action , Click OK on the " door open" error. "Continue task after error" checked so it continues to 4) if there was no error!
4) AutoInput Action, Click heater button
That's it..

Worked nicely so far.
Note also that I don't have any waits and it still works nicely. Autoinput Actions have timeouts builtin, I used the default 20 second. The task waits 20 seconds at 3) if there is no error, and then proceeds to 4..
2) is not even really needed because app is already visible, but "just in case"..
I didn't bother turning Wifi on and off, I don't know if it makes big difference to battery life.. Also no need to turn on the display, it will stay up for 1min after the call.
I used the AutoInput's "Easy Setup" -function to get actual id's of the buttons, and then click those instead of coordinates or text labels.