The only constitutional issue with taxing energy exports is gettin Congress to pass the law and POTUS to sign it.
“No Tax or Duty shall be laid on Articles exported from any State” [1].
[1] https://constitution.congress.gov/constitution/ Art. I § 9
They can just outlaw exporting energy, but not tax it.
“No Tax or Duty shall be laid on Articles exported from any State” [1].
[1] https://constitution.congress.gov/constitution/ Art. I § 9