Get a Battleship or bigger into orbit of an enemy planet. Not sure if in this Orion bigger planets require bigger ships.

Looks like battleship is it, someone also posted that you need at least 1 bomb.

Mind control seems quite overpowered if it's similar to MoO2, instantly getting full control.

Firstly, the battleship should be equipped with some "Telepath chambers" that take up space. Can't imagine the crew would just casually mind control billions of people while doing their other duties. A powerful effect like that surely needs a price tag.

Secondly, the mind control should be broken if the ship leaves the orbit. That wouldn't stop the Elerians from mind controlling a colony for a few turns, exploiting it as they please and then scuttling whatever they want - or invading it properly without resistance.