Maybe it would be easier to do it the other way:
Beer Wagon - $4
Treasure- Reaction
Worth $2
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At the beginning of your turn, you may reveal and discard this card.
If you do: +1 Card, +2 Actions
It loses the ability to choose to use it for actions after seeing what you get from other actions, but if you're trying to use it as a village you'd likely want to start with it.
If you can discard it at any time, it should definitely cost $5 because its too good. As it is, maybe fine.
It will also cause some confusion with "at the beginning of your turn" duration card effects (because in general you would choose the order of "beginning of turn" effects, but this is not an effect until you actually do it, so, after drawing for previous turn Wharf, is it still the beginning of turn?).
Discarding it may create infinite loops (for instance, if you have a 5-card deck, you can discard it and redraw it as much as you want, and then play a Diadem for infinite money). You should set it aside until the end of the turn or something like that.