The interface for Hamlet has changed, as you noted.
When you want to discard for both effects, choose "Discard for Action", the select the card you want to discard (for +1 Action). Afterwards you will be given the option to "Discard for Buy".
It's a bit more cumbersome this way, but it allows correct interactions, as the discards are now consecutive (as they are supposed to be) instead of simultaneous (as before).
In all cases, you can just continue playing cards from your hand if you don't want to use any (more) discard effects of Hamlet.