why is it almost essential to assume that hamlet had overheard Polonius' plans, or that he became aware of the presence of Polonius and Claudius?

Hamlet says things that were meant for Polonius to hear. When he clues in that his meeting with Ophelia is a set up, his language is charged at her father and Claudius more than Ophelia. Ophelia is just collateral damage in his rant, "Let the doors be shut upon him, that he may play the fool no where but in ’s own house."