I don’t know what to make of the beaten way of friendship. It feels like Hamlet is appealing to the shared history he has with Rosencrantz and Guildenstern, appealing to their previously established bonds of friendship.
I think of a path between houses in a wood. At first the path between the two friend’s homes requires a bit of bushwacking but over time, with all the coming and going, the visiting and such, the path gets clearer, wider, the dirt beaten down until it is almost paved. I might call it s well-trodden path of affection between us. As such, the beaten way is a quite lovely idea – but it does feature the word BEATEN, which calls to mind more violent associations. Is it possible that Hamlet means to both threaten and appeal to their shared history?
In any case, he does need to work out what they’re doing there.