I don't really think it matters what you're discarding the card for. If you actually do discard for the extra action, then it's no different from if you had gotten the +Action for free and discarded for the extra card instead. I'm more concerned with the actual effect than the exact text on the card.
If you always got +Action and you could optionally discard to draw a card, sure, that second part is sifting. Except that's not what the card does. The actual effect is that you get the card either way and you can discard for Action or Buy. That is discard for benefit. The initial +1 Card has no bearing on it.
[/quote]Sure, if you just play it as a cantrip then it doesn't sift at all, but if you actually use 1 of the discard effects then you've gotten part of the Festival effect, you end with the same handsize as if you had played Festival, but unlike Festival you've been given the opportunity to choose the best 4 out of 5 instead of just being stuck with some 4-card hand. So I don't see how you figure that Hamlet does no more sifting than Festival. Cartographer doesn't let you draw extra cards if you discard, but it's still a sifter.[/quote]
Cartographer is a sifter because the discarding improves what you will draw. Hamlet is not a sifter because the discarding doesn't have an impact on that at all, any more than Secret Chamber does.
I mean, right now you are arguing that Hamlet is a sifter based on something that Hamlet literally does not do (switching a bad card for a good card). It's like saying Baron is a money-generating card that lets you discard for +1 Buy.