Unfold in all directions
SOGL V0.12, 75 bytes
l√u²m√lH»{ā;l⁾:A∫Ba{bIwFIWhFbž;FIbI@ž}};}¹K⁴{ē2\⌡±e{@Κ};⁴┼┼};0E{ē2\⌡№:h++}╚

Try it Here!
This expects the input on the stack, so for ease-of-use I added , at the start. That can cause issues if the input contains only numbers so here
is a a test-suite for that.
70 bytes √lH»{ā;l⁾:A∫Ba{bIwFIWhFbž;FIbI@ž}};}¹K⁴{ē2\⌡±e{@Κ};⁴┼┼};0E{ē2\⌡№:h++}╚ works too, but as I only now implemented √ on strings and the documentation didn't mention that it would floor the length I won't count it.
Explanation:
creating a square from the input

l       get the length of the input
 √      get its square root
  u     floor that
   ²    square it
    m   mold the input to that length
     √  convert it to a square

creating the unfoldings of the square - the idea is to cut out the inner squares to a new array

lH»{                              } (length-1)//2 times do
    ā;                                push an empty array below ToS
      l⁾                              push ToS.length - 2 (ToS here is the square or the previous unfolding)
        :A                            save a copy of that in the variable A
          ∫B                    }     repeat that amount of times, saving iteration on B - cutting the inner square to the empty array
            a{                 }        variable A times do
              bIw                         get the b+1th row of the previous unfolding
                 FIW                      get the (current loops iteration + 1)th character of that
                    h                     swap the 2 items below ToS - so the stack now is [..., prevUnfolding, newArray, character]
                     Fbž                  at [current loops iteration; b] insert that character in the array
                        ;                 swap the top 2 items - the stack now is [..., newArray, prevUnfolding]
                         FIbI@ž           at [current loops iteration+1; b+1] insert a space
                                 ;    get the now not empty array ontop of the stack

add the horizontal unfoldings

¹                    wrap the stack in an array
 K                   push the 1st item of that, which will function as the canvas
  ⁴{              }  iterate over a copy of the remaining items
    ē2\⌡               repeat (e++ divides by 2) times (default for the variable E is the input, which defaults to 0)
        ±                reverse the array horizontally
         e{  }         repeat e times
           @Κ            add a space before ToS
              ;⁴┼┼     add that horizontally before and after the canvas

add the veertical unfoldings

;                get the copy of the foldings above the canvas
 0E              reset the variable E to 0
   {         }   iterate the copy of the foldings
    ē2\⌡           repeat (e++ divides by 2) times (default for the variable E is the input, which defaults to 0)
        №            reverse the array vertically
         :h++      add that vertically before and after the canvas
              ╚  center the canvas vertically