Why is it that some objects don't have a databaseId field in V4 API?

Some objects such as Labels or Milestones do not expose their databaseIds in the graphql API the way other objects do (e.g. Repository and Issue ).

Is there any way to access their databaseId in V4?

Will all the databaseId fields eventually get depracated from V4?

Not sure why you need those but try using id instead.