Static sizing information lost with structured matrices

It seems that Base's structured matrices when wrapping static matrices inconsistently propagate that size information to output types of functions on v0.12.3. e.g.

julia> x = @SMatrix randn(3, 3)
3×3 SArray{Tuple{3,3},Float64,2,9} with indices SOneTo(3)×SOneTo(3):
 -1.6129    -0.686314  -1.42919
  0.289051   0.192384   0.170077
  0.877949   0.25176   -0.0438329

julia> s = Symmetric(@SMatrix randn(3, 3))
3×3 Symmetric{Float64,SArray{Tuple{3,3},Float64,2,9}}:
 0.32467   0.193486   0.426171
 0.193486  0.111974   1.33137
 0.426171  1.33137   -0.731089

julia> x * s # size information lost
3×3 Array{Float64,2}:
 -1.26553   -2.2917    -0.55625
  0.203552   0.303905   0.254978
  0.315075   0.139704   0.741387

julia> x + s # size information kept
3×3 SArray{Tuple{3,3},Float64,2,9} with indices SOneTo(3)×SOneTo(3):
 -1.28823   -0.492828  -1.00301
  0.482537   0.304358   1.50145
  1.30412    1.58313   -0.774922

Reproduce the issue in Julia v0.12.3 using @SMatrix with Symmetric, then compare the output types of multiplication and addition. Trace the relevant StaticArrays methods for these operations and verify that multiplication preserves static size information, with tests covering both examples.