More than fifty years after the Second World War, a number of African American soldiers were awarded, some of them posthumously,
with the Congressional Medal of Honor, which was the nation’s highest military award, and which was long overdue in recognition of their outstanding bravery.
Option Elimination -
(A) with the Congressional Medal of Honor, which was the nation’s highest military award, and which was long overdue in -
"awarded" is the right usage without "with." I am happy to see if someone can tag from Oxford, Cambridge, or other authentic sources. I tried multiple sentences available online, but nothing works with "with." I apologize for my ignorance, so please share your source
Usage of "awarded" - "awarded" means to grant or present something to someone due to their achievements or actions. E.g., She was awarded a scholarship for her academic excellence.
Another issue here is "was." The medal is still the nation's highest military award. Using two relative clauses that refer to the same noun, "the Congressional Medal," is a bit inferior to the flexible modifier (if you like jargon, then appositive

construction in option E).
(B) with the Congressional Medal of Honor, the nation’s highest military award for long-overdue - "in recognition" is better.
(C) the Congressional Medal of Honor, which was the nation’s highest military award, long-overdue in - "was" issue.
(D) the Congressional Medal of Honor, the nation’s highest military award for long-overdue - "in recognition" is better.
(E) the Congressional Medal of Honor, the nation’s highest military award, in long-overdue - ok