What are you running it off? Solar power going into a battery bank and then running it directly off the battery pack into the satellite? Does it move or is it stationary? I cannot think why it would use as much energy as you say because if it does not have a motor it should just be pointing at the satellite and if that does not move it just sends the connection back. If it has a motor and follows the satellite I can see why it would use a lot of energy.
I believe it does a fair chunk of processing to derive the signal, it's not like an old-style satellite dish, In addition, TCP is a chatty protocol. I'm not sure if Starlink does tricks with that (my old Starband system did but that was for geostationary orbit where latency was to be avoided).