Occupation type seems to represent this mechanic. If you could create puppets out of occupied territory you would seriously just get to freely annex territory into a puppet whenever you want. That's pretty OP honestly. There's no reason Occupation Policy can't fill these shoes and potentially be fleshed out to be more accurate (IE adding a puppet leader which gives different effects on the land he oversees).
Sorry, but I really think you ought to give HOI2 a spin so you can see how this works: not OP, and not addressed by the occupation mechanic at all.
PS - kind of curious about what is wrong with "annex[ing] territory into a puppet whenever you want". This is what occurred historically, particularly in territories conquered by the Japanese. Even if the game didn't impose any cost for releasing puppets (HOI2 imposed a dissent cost), it is not "free" in any real sense because you still loose the advantages of occupying the territory. The only thing that need be added is a nerf for puppets.
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