Disambiguate division and pseudo-division?

...where division means "equivalent to multiplication with inverse" and pseudo-division means "equivalent to multiplication with pseudo-inverse" (with equivalence neglecting any numerical issues). Briefly came up in JuliaLang/julia#23067. Motivating example:
```julia
julia> using LinearAlgebra

julia> foo(n) = zeros(n, 3) \ zeros(n, 1)
foo (generic function with 1 method)

julia> foo(1)
3×1 Array{Float64,2}:
0.0
0.0
0.0

julia> foo(2)
3×1 Array{Float64,2}:
0.0
0.0
0.0

julia> foo(3)
ERROR: SingularException(1)
Stacktrace:
[1] ldiv!(::Diagonal{Float64,Array{Float64,1}}, ::Array{Float64,2}) at stdlib/v1.1/LinearAlgebra/src/diagonal.jl:438
[2] \(::Diagonal{Float64,Array{Float64,1}}, ::Array{Float64,2}) at stdlib/v1.1/LinearAlgebra/src/diagonal.jl:445
[3] \(::Array{Float64,2}, ::Array{Float64,2}) at stdlib/v1.1/LinearAlgebra/src/generic.jl:862
[4] foo(::Int64) at ./REPL[2]:1
[5] top-level scope at none:0

julia> foo(4)
3×1 Array{Float64,2}:
0.0
0.0
0.0
```

Here, it would be useful if there was a dedicated operator to ask for the least-squares solution. But if there was one, `\` should probably always mean exact solution and fail for rectangular matrices.

So if we do this, it would be quite breaking. Is it justified? Should we explore this?