I got the answer by looking at NavigatorWindow. Posting here in case anybody needs to do this in the future.
- Call DockingManager.Layout.Descendents().OfType<LayoutAnchorable>() to find the LayoutAnchorable that has a ContentId matching the expected one
- Get the LayoutItem by calling DockingManager.GetLayoutItemFromModel()
-
Call LayoutItem.ActivateCommand.Execute(null) to select the item and give it focus.