OP, I think the best thing would be to call tesla energy support over the phone. It appears to me, that what I would call "web tickets" (those coming in from the app) seem to go into a big bucket and get worked on while reps are in between other phone calls.
I say this as someone who still gets work escalated to them through a ticketing system myself. There are plenty of ways for someone in our company to "contact the help desk" (which isnt me), but the "fastest" way is to call, and have the help desk person either help you or not be able to help you, and put notes in their ticket, and escalate it.
Thats always faster at my company than simply submitting a ticket via the web interface, but people continue to submit over the web because "its easier" even if I tell them "only do that if you dont mind waiting to hear the answer for a while".
I dont work at tesla but my experience in dealing with them suggests its very similar to the above.
TL ; DR, dont bother using the app to submit a ticket unless you dont mind waiting for "whenever". Call energy support, get a human and have them escalate.