Inconsistent output types of SMatrix solve with Vector/Matrix rhs

Consider the following example:

P = @SMatrix [-0.5 0.5 0.5; 0.5 -0.5 0.5; 0.5 0.5 -0.5] # SMatrix{3,3,Float64,9}
w = rand(Float64, 3)    # Vector{Float64}
W = rand(Float64, 3, 3) # Matrix{Float64}

println(typeof(P\w)) # => SArray{Tuple{3},Float64,1,3}
println(typeof(P\W)) # => Array{Float64,2}

i.e. doing a matrix solve with \(::SMatrix, ::Matrix) returns an ordinary matrix but a matrix solve with \(::SMatrix, ::Vector) returns a static vector. This seems surprising to me: I had expected both calls to return non-static/ordinary vectors/matrices (or at least the same "base" array type).

Here, \ calls into the generic (\)(A::AbstractMatrix, B::AbstractVecOrMat) from LinearAlgebra (at https://github.com/JuliaLang/julia/blob/cf410dc9e81cfa14a18ca3aef50346000b4615c7/stdlib/LinearAlgebra/src/generic.jl#L1102) which in turn calls into StaticArrays' \ method for LU decompositions at https://github.com/JuliaArrays/StaticArrays.jl/blob/64c64b2d808eed0b5751d080205ae2efe218f57e/src/lu.jl#L186-L187

So the issue seems to me that v[F.p] in the above converts v to an SVector (due to the indexing call), but B[F.p,:] is still an ordinary matrix due to the combination with :.

Reproduce the Vector and Matrix right-hand-side cases from the issue, then inspect the StaticArrays LU solve methods around src/lu.jl:186-187 and the generic LinearAlgebra method referenced in the report. Check how v[F.p] and B[F.p,:] are constructed, and add regression coverage showing consistent output types for both calls. Done means the two solve forms follow the same intended array-type behavior.