The court's appointment under 28 U.S. Code § 546 was described as "seldom-used" and "very unusual".
Not so rare in 2022 with about 30 current appointments, though likely far more earlier this year. The number may have been as high as 56 because Biden asked all Trump appointed and confirmed U.S. Attorneys to resign and the Senate filibuster affects how long it takes for an acceptable nominee to be confirmed. (It is likely that a similar high number occurred with the 2017 dismissal or resignation of 46 U.S. Attorneys with 47 posts already vacant or open by prior resignations.)
Q: Just how often are U.S. Attorneys appointed by courts and is there such a list?
Firstly, I could find no list. Secondly, how often becomes irrelevant when mass removal of U.S. Attorneys takes place. Thirdly, even common sources are not always clear as to whether current U.S. Attorneys, not appointed by the president, became U.S. Attorneys by appointment by the courts.
Under 28 U.S. Code § 546, concerning appointment by the Attorney General (AG),
(c) A person appointed as United States attorney under this section may serve until the earlier of—
(1) the qualification of a United States attorney for such district appointed by the President under section 541 of this title; or
(2) the expiration of 120 days after appointment by the Attorney General under this section.
(d) If an appointment expires under subsection (c)(2), the district court for such district may appoint a United States attorney to serve until the vacancy is filled. The order of appointment by the court shall be filed with the clerk of the court.
It follows that, if a source notes that the AG made an appointment and more than 120 days have lapsed, then continuation of service in the position of U.S. Attorney must have been approved by the court under section (d).
The estimate of about 30 current appointments was determined by comparing two lists and reviewing some biographies.
Using the Wikipedia List of United States attorneys appointed by Joe Biden, one may see that, as of this writing, there are 40 U.S. Attorney positions for which no presidential appointment has been made (there are some nominees with AG appointments). Each of these may have a U.S. Attorney appointed by the court. By comparing the above list with U.S. Attorneys Listing, September 28, 2022, one may find links to the bios of each of the U.S. Attorneys often describing their appointment.
For Alabama's three districts, Biden has yet to make any appointment (TBA). Following the links from the latter listing, Sandra Stewart was appointed by the court, Prim F. Escalona was appointed more than 120 days ago, and Sean Costello was appointed by an Acting Attorney General more than 120 days ago. It is not clear how Escalona was appointed and, to comply with the law, Costello's appointment would have to been extended by the court.
Results similar to Alabama's occur with comparisons to other U.S. Attorneys' positions for other states.