Full Q factor in QR not created

[kellertuer]

Consider the following code

using LinearAlgebra, StaticArrays
a = [0.8045637657777136 -0.5871860208192704; -0.5920697370223342 -0.7814816517349663; 0.046158133626574324 0.21094787260368533 ]
p = SMatrix{3,2}(a...)
b = [0.0902581948780876 0.971125474230239; 0.7756374067122164 -0.2076324892367811; 0.971125474230239 0.1174906920331621 ]
q = SMatrix{3,2}(b...)

M = p' * q
QR = qr(q - p * M)
V = convert(Matrix, qr([M; QR.R]).Q * I) # should be 4x4 is 4x2

M2 = a' * b
QR2 = qr(a - b * M2)
V2 = convert(Matrix, qr([M2; QR2.R]).Q * I) # correct form

Note especially that the inner qr has two different types

julia> qr([M; QR.R]).Q
4×2 SMatrix{4, 2, Float64, 8} with indices SOneTo(4)×SOneTo(2):
 -0.274279   0.919138
 -0.364558  -0.371476
 -0.88987   -0.131115
  0.0       -3.54073e-16

julia> qr([M2; QR2.R]).Q
4×4 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}}:
 -0.224564   0.45094    -0.708849  -0.493718
 -0.29848   -0.206537   -0.557078   0.746938
 -0.927621  -0.0427088   0.350853  -0.120819
  0.0        0.867278    0.253177   0.428637

So how can I get the full form for both in a unified form?