Branch, 35 bytes

/;{^\;{Z[{Z0]z^[/@^\@^0]~`L`Ln[0`P] 

Try it on the online Branch interpreter!

Of course, it's only natural that a language based on binary trees would have a way to solve this challenge. Branch is still in development; I'm not sure how I could've solved this before adding a bunch of bugfixes and a couple of new helpers.

Pretty-printing the tree was actually around from the start though. I used it as a debug feature; never thought I would've found a challenge so soon to use a debug feature as output formatting for :P