Oswald was added to Disney Dreamlight Valley on May 1st in the A Rift in Time, A Spark of Imagination expansion update. Unfortunately, unlocking him is a tricky business, as you'll need to complete several missions and then retrieve him from the ancient ruins.
How to UNLOCK OSWALD (ALL PUZZLES SOLVED) | Dreamlight Valley
To get Oswald out of the ancient ruins, you'll need to complete the A Spark of Imagination quest, which starts once you've completed the A Bit of Help From Your Friends quest. Everything is connected, which makes it confusing. But as long as you've completed the A Spark of Imagination quest and left the ruins, you can unlock Oswald.
You can unlock Oswald in Disney Dreamlight Valley by completing his quest, Oswald's Many Dimensions. This quest is not automatically assigned to you like it was with the Monochrome Mystery, which begins once you complete A Spark of Imagination.
Once you both leave the ancient ruins and see the monochrome tears, you can find Oswald on the Eternity Isle, talk to him and begin his quest.