Apparently the process is not defined by anything more than that it’s a simple majority vote by both houses. There’s no way an EO would be considered legal, but I take your meaning that this whole charade is extra-Constitutional on its face.
Official admission to the Union requires Congress to draft — and the president to sign — a bill called an “enabling act.” For Puerto Rico to become a state, it would need to convince Congress and the president that statehood is not only in the best interest of the Puerto Rican people, but in the best interest of the United States as a whole. The U.S. Senate and the House of Representatives would need to approve the statehood admission by a two-thirds majority vote [source: The Week].
https://people.howstuffworks.com/new-state-in-us.htm