>> And among equal branches of government, SC Justices are free to give remarks on matters not formally before the Court. <<
Not exaaaaaaactly. They can comment on judicial philosophy or news or whether the Redskins will ever make it to the playoffs, but they will not comment on matters that are plausibly about to be before the court, either. This would seem likely to be among such matters.
Presumably, the letter’s content did not reference any matter before the court or possibly in the future regarding un-recusal as court approval is not necessary in that context. The educated guess is that the letter notified of a case where original jurisdiction was warranted.
For all we know, the letter may have been a notification of the AG’s intention to file for trials of foreign agents.
As for Sessions un-recusal, no SCOTUS involvement is necessary other than a courtesy notification of intent to pursue matters previously recused from.
The White House as an equal branch of federal government can go directly to SCOTUS bypassing all lower courts in matters it deems important and constitutional. Presumably, therefore, the AG’s letter was a notification that the AG would file a direct Petition for Certiorari in cases of original and exclusive jurisdiction. Two justices would review and approve or disapprove of such cases going forward.
Art. 3, Sec. 2
“In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the Supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the Supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.”
One guess is that the mentioned letter of Sessions described an intent to prosecute foreign actors such as Steele, Mifsud, Halper, Downer, Johnson, others that were engaged in a plot of overthrow the duly elected President.
The mentioned letter mentions it was classified in terms of recusal-unrecusal and presumably sought clarity in matters of conflicts based on declassified materials.
There is absolutely no restriction whatsoever for a cabinet head to seek clarity from SCOTUS over potential matters of original and exclusive jurisdiction.