Learn English – Meaning of “I’m deep in the mountains”

While some of the definitions and idioms mentioned/linked are relatively close approximations, they all miss the specific idiom "in too deep", referenced here: (to) be in too deep

This generally references being involved in something so thoroughly that you become unable to extricate yourself (you can't escape); it is meant to allude to the experience of being in a mud bog or shallow quicksand (not enough to bury you, but too deep to escape), or to wander into a cave or woods so far that you no longer know how to return.

Note this is not precisely the same meaning as being "in deep water" or "being thrown into the deep end"; these latter two idioms indicate overwhelming challenge or great difficulty, or being forced to face a challenge beyond your experience or comfort.

I take it to mean that there were three stacks of books (each stack being of indeterminate height), one behind another.

To give some cheap ASCII art of it:

||
wall
|| [[[[       ]]]]    :::::
||  AAAAA   BBBBBB    CCCCCC
|| @@@@@    #####    $$$$$$$$               Harry stands here, 
||  1111   2222222  3333333              <- looking that way
|| abooka  bbbookb   ccbookc
===============================mantel==  
   stack 1 stack2    stack3

In the above "art", the books are stacked five high and three deep (from Harry's perspective). There's probably room for another stack, which would then make the stacks four deep; and you could pile on as many more books as you want (until they fall over), making the stacks 15 high or more.