Andrew,
There is no such thing as a type rating for something like a C172. You may have a type checkout - in fact, most clubs or insurance companies would insist on it - but there's no legal requirement to do so.
What you must do is make sure you're familiar with the systems of any new aircraft you fly.
If you happen to have a chance to fly a normally-aspirated petrol-engined C172 (note I'm being very careful about specifying the details here - the C172 I fly is fuel injected, and so doesn't have a carb heat control!) and all the aircraft you've ever flown have had FADEC, then even if your insurance company or the aircraft owner didn't explicitly say so, you would have a duty to ensure that you understood that aircraft's systems before you flew it. The same would apply to any new type, or even any new aircraft even if you're familiar with the type.
Depending on how complex the systems are compared to what you're used to, that might involve some dual time with an instructor, or it might be ground time with an instructor, or it might just be your reading the manuals. Admitedly in the case of carb heat and mixture, you reading the manuals probably isn't enough, but legally there's nothing that stipulates that.
You say that "learning how to use mixture/carb heat and so on is normally taught during PPL". There is nothing on the PPL syllabus which specifies that you must learn to use mixture and carb heat. However, you must learn to operate the aircraft you'll be using for your test - if that aircraft has a mixture control and a carb heat control, then you must learn to use them, otherwise you don't have to. Likewise, if do your test on a tail-wheel aircraft you must learn to do 3-point landings, otherwise you don't have to. And if the aircraft you use for your test has flaps you must be able to use them, but if it doesn't, you don't have to.
To compare to the world of driving, you don't need to learn to double-declutch in order to pass a driving test. On the other hand, if you (are mad enough to) choose to take your driving test in an early 20th century car without synchro-mesh then you will have to learn to double-declutch. If you choose to buy such a car after your test, then you will learn to double-declutch as you learn to drive the new car.
FFF
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