The fact that Williams has now been nominated for all of the OT and all of the ST makes his complete shut out from the PT all the more questionable. I think perhaps the only explanation is he had other scores those years that the Academy was more interested in.
Angela’s Ashes in 1999, Catch Me If You Can in 2002, and both Memories of a Geisha and Munich in 2005.
https://en.wikipedia.org/wiki/List_of_awards_and_nominations_received_by_John_Williams
In 2002, he also had Minority Report and Harry Potter and the Chamber of Secrets go unnominated, and War of the Worlds in 2005.
https://en.wikipedia.org/wiki/List_of_compositions_by_John_Williams#Film_scores