Transpose in arrays of n columns

A nice piece of work!  To my mind this is an example of Excel formulas as they should be. 

A million miles from the traditional spreadsheet!

This solution is from a past discussion concerning Thunks.

=ReShapeMatrixλ(data, 3, 3)

ReShapeMatrixλ gets an assist from Peter's EVALTHUNKARRλ -

//Re-shape a matrix by specifying width and depth. 'shape' - 0 to vertically stack arrays,
//1 to horizontally stack arrays. 'shape' defaults to vertical stack if omitted.
//'pad_with' defaults to "" if omitted.

ReShapeMatrixλ = LAMBDA(matrix, depth, width, [shape], [pad_with],
        LET(

//Prevent uneven distribution of rows and/or columns by
//ensuring dimensions are properly rounded according to
//depth and width.
            i, CEILING.MATH(ROWS(matrix), depth),
            j, CEILING.MATH(COLUMNS(matrix), width),

//Set padding and expand matrix as needed.
            padding, IF(ISOMITTED(pad_with), "", pad_with),
            M, EXPAND(matrix, i, j, padding),

//Create two matrices which serve as row and column coordinates
//for INDEX.
            M_rows, SEQUENCE(i / depth, , , depth) * SEQUENCE(, j / width, , 0),
            M_cols, SEQUENCE(, j / width, , width) * SEQUENCE(i / depth, , , 0),

//Generate 'r' and 'c' coordinates based on starting row (v₁) and column (v₂).
//Retrieve 'block' from matrix as a vector and stuff in a thunk.
            CreateVectors, LAMBDA(v₁, v₂,
                LET(
                    r, TOCOL(SEQUENCE(depth, , v₁) * SEQUENCE(, width, , 0)),
                    c, TOCOL(SEQUENCE(, width, v₂) * SEQUENCE(depth, , , 0)),
                    block, INDEX(M, r, c),
                    THUNK(block)
                )
            ),

//Map and convert to vector to prepare for unpacking.

            thunks, TOCOL(MAP(M_rows, M_cols, CreateVectors)),

//Unpack thunks.

            unpacked, EVALTHUNKARRλ(thunks),

//Wrap vector according to desired shape.
            vshaped, WRAPROWS(unpacked, depth * width),
            hshaped, WRAPCOLS(unpacked, depth * width),
            reshaped, IF(
                ISOMITTED(shape),
                vshaped,
                IF(shape, hshaped, vshaped)
            ),
            reshaped
        )
    );

Another potential option, using TRANSPOSE and PIVOTBY, plus a few extra steps to sort the results and rearrange the header rows:

=LET(
    arr, TRANSPOSE(A1:G5),
    pvt, DROP(PIVOTBY(SCAN("",TAKE(arr,,1),LAMBDA(a,v,IF(v="",a,v))),INDEX(arr,,2),DROP(arr,,2),SUM,3,0,,0,-1),1),
    srt, SORTBY(pvt,INDEX(pvt,2)),
    grp, INDEX(srt,2),
    VSTACK(IF(grp<>HSTACK("",DROP(grp,,-1)),"Group "&grp,""),TAKE(srt,1),DROP(srt,2))
)

Note: the SCAN function used in the row_fields argument of PIVOTBY assumes the "Grade" headers shown in your raw data screenshot have Merge & Center formatting applied (they appear to, considering the vertical gridlines are not visible).

I throw another option into the ring.  I was about to add it when I saw Peter dropped his so I used his workbook and combined all 3 on this workbook.

This option is:

=LET(in, B3:M7, cols, 3,
DROP(REDUCE("",SEQUENCE(ROWS(in)),
   LAMBDA(p,q,HSTACK(p,WRAPROWS(CHOOSEROWS(in,q),cols,0)))),,1))

simply each ROW uses WRAPROWS to create the columns needed and stack to the right.

This formula uses a complicated function to expand thunks.  Otherwise switching the order of the dimensions in a multidimensional array requires sorting by index.

= EVALTHUNKARRλ(TRANSPOSE(BYROW(rng, LAMBDA(d, LAMBDA(WRAPROWS(d, cols))))))

=LET(cols,3,

rng,B3:M7,

DROP(REDUCE("",SEQUENCE(1,COLUMNS(rng)/cols,1,cols),

LAMBDA(u,v,

VSTACK(u,

TOROW(CHOOSECOLS(rng,SEQUENCE(1,cols,v)))))),

1)

)

This formula works in Office 365 and Excel for the web and returns the intended result in my example. You dynamically change the number of columns in the formula.