Unexpected output types from `inv(transform)(x)`

Consider the following

using CoordinateTransformations
using GeometryBasics
using LinearAlgebra
using Rotations

# define transformations
s = LinearMap(Diagonal(Vec3f(1,1,2)))
r = LinearMap(RotX(0.5f0 * π))
t = Translation(Vec3f(0,1,0))
srt = t ∘ r ∘ s

# vector to be transformed
p = Vec3f(1,2,3)

# display type of transformation output
@show typeof(s(p))
@show typeof(r(p))
@show typeof(t(p))
@show typeof(srt(p))
@show typeof(inv(s)(p))
@show typeof(inv(r)(p))
@show typeof(inv(t)(p))
@show typeof(inv(srt)(p))

I was expecting that the output types of all transformations above would be Vec{3, Float32}, but for the inverse transformations I see multiple different output types.

typeof(s(p)) = Vec{3, Float32}
typeof(r(p)) = Vec{3, Float32}
typeof(t(p)) = Vec{3, Float32}
typeof(srt(p)) = Vec{3, Float32}
typeof((inv(s))(p)) = StaticArrays.MVector{3, Float32}
typeof((inv(r))(p)) = Vec{3, Float32}
typeof((inv(t))(p)) = Vec{3, Float32}
typeof((inv(srt))(p)) = Vector{Float32}

Reproduce the reported behavior with the Julia snippet in the issue, focusing on the output types of the forward and inverse transformations. Compare the results for LinearMap, Rotations, Translation, and the composed transformation; done means the inverse behavior is understood and the inconsistent output types are addressed or documented.