He's doing Oppenheimer (out July 2023), and Wakanda Forever was released in November 2022. That's more work than Creed III.
After working with Nolan and winning 2 Emmys, the Mandalorian is probably not a priority for him anymore, and requires a lot more work than a film.
Joseph Shirley was recently listed on IMDB as the composer of S3. Also he retweeted the trailer. Ludwig is silent about it, and said it's a secret when asked about it.